Maths-
General
Easy
Question
The figure above shows that the shaded triangular region with a hypotenuse of 5 centimeters (cm) has been removed from a rectangular tile with dimensions x cm by y cm. of the following, which best approximates the area, in square centimeters, of the tile before the piece was removed?
- 15
- 43
- 50
- 65
The correct answer is: 65
HINT: Find the measure of other angles and hence find the sides.
Complete step by step solution:
Given that ∠CAE = ∠EAF = ∠FAB = 30°
Also, ∠ACE = ∠AEF = ∠ABF = ∠EDF = 90°
So, we have ∠CEA = ∠AFE = ∠AFB = 180 - (90 + 30) = 60°
From this, we get ∠EFD=60° (supplementary angles,180 - (60 + 60)) and ∠DEF=30°
(In △EDF, ∠DEF = 180 - (60 + 90) = 30°)
Here, we have four 30 - 60 - 90 triangles ΔACE, ΔAEF, ΔAFB, ΔEDF.
In △AEF, we have shorter side (EF) = 5
Then, AF = 2 × 5 = 10 (In 30 - 60 - 90 triangle, the hypotenuse is twice the shorter side)
And the longer side AE = 
(In 30 - 60 - 90 triangle, the longer side is 
times the shorter side)
In △ACE, we have hypotenuse AE =
Then, the shorter side CE = 
(In 30 - 60 - 90 triangle, the shorter side is half the hypotenuse)
And the longer side AC = 
(In 30 - 60 - 90 triangle, the longer side is times the shorter side)
In △AFB, we have hypotenuse AF = 10
Then, the shorter side FB = 5 (In 30 - 60 - 90 triangle, the shorter side is half the hypotenuse)
And the longer side AB = (In 30 - 60 - 90 triangle, the longer side is times the shorter side)
Now, we have x = and y =
Area of the rectangle = xy = × = 64.95 which can be rounded to 65 cm2
Hence option D is the correct answer.
Related Questions to study
Maths-
The polynomial p4 + 4p3 + 3p2 - 4p - 4 can be written as (p2 - 1) (p + 2)2. What are all of the roots of the polynomial?
The polynomial p4 + 4p3 + 3p2 - 4p - 4 can be written as (p2 - 1) (p + 2)2. What are all of the roots of the polynomial?
Maths-General
Maths-
2x + 3y = 5
4x + cy = 8
In the system of equations above, c is a constant. For what value of c will there be no solution (x, y) to the system of equations?
2x + 3y = 5
4x + cy = 8
In the system of equations above, c is a constant. For what value of c will there be no solution (x, y) to the system of equations?
Maths-General
Maths-
A project coordinator at a banquet hall is given the task of arranging seating for an awards ceremony. The figure above shows the first three possible arrangements of tables and the maximum number of seats in each arrangement. If the number of seats in each successive arrangement is increased by 6 over the preceding arrangement, which of the following represents the maximum number of seats around n tables?
A project coordinator at a banquet hall is given the task of arranging seating for an awards ceremony. The figure above shows the first three possible arrangements of tables and the maximum number of seats in each arrangement. If the number of seats in each successive arrangement is increased by 6 over the preceding arrangement, which of the following represents the maximum number of seats around n tables?
Maths-General
Maths-
If 2
= a, what is 2x in terms of a ?
If 2 = a, what is 2x in terms of a ?
Maths-General
Maths-
During a storm, the atmospheric pressure in a certain location fell at a constant rate of 3.4 millibars (mb) per hour over a 24-hour time period. Which of the following is closest to the total drop in atmospheric pressure, in millimeters of mercury (mmHg), over the course of 5 hours during the 24-hour time period?
(Note: 1,013mb = 760 mmHg )
During a storm, the atmospheric pressure in a certain location fell at a constant rate of 3.4 millibars (mb) per hour over a 24-hour time period. Which of the following is closest to the total drop in atmospheric pressure, in millimeters of mercury (mmHg), over the course of 5 hours during the 24-hour time period?
(Note: 1,013mb = 760 mmHg )
Maths-General
Maths-
Ryan has 1,500 yards of yarn. He wants to knit at least 2 scarves and at least 3 hats. Each scarf requires 300 yards of yarn, and each hat requires 120 yards of yarn. If s represents the number of scarves and h represents the number of hats, which of the following systems of inequalities represents this situation?
Ryan has 1,500 yards of yarn. He wants to knit at least 2 scarves and at least 3 hats. Each scarf requires 300 yards of yarn, and each hat requires 120 yards of yarn. If s represents the number of scarves and h represents the number of hats, which of the following systems of inequalities represents this situation?
Maths-General
Maths-
Tara rode her bicycle along a straight road from her home to a restaurant and ate lunch. She then continued along the same road to a movie theater to see a movie. Finally, she returned home on the same road after the movie. Tara's distance from home during the 4 hours she was out is shown in the graph above. How many total miles did she ride her bicycle?
The connection length between the two points of the line segment is used to measure the distance between them. The length of the line segment, the shortest distance between a point and a line, is the separation between them.
¶The path length between two points is known as the distance. The meter serves as the SI unit for distance.
¶A scalar quantity, distance. The entire path of an object has taken to define distance. An illustration. If a turn is taken to head north for an additional 8 km, a car must travel a total of 13 km if it travels east for 5 km first.
Tara rode her bicycle along a straight road from her home to a restaurant and ate lunch. She then continued along the same road to a movie theater to see a movie. Finally, she returned home on the same road after the movie. Tara's distance from home during the 4 hours she was out is shown in the graph above. How many total miles did she ride her bicycle?
Maths-General
The connection length between the two points of the line segment is used to measure the distance between them. The length of the line segment, the shortest distance between a point and a line, is the separation between them.
¶The path length between two points is known as the distance. The meter serves as the SI unit for distance.
¶A scalar quantity, distance. The entire path of an object has taken to define distance. An illustration. If a turn is taken to head north for an additional 8 km, a car must travel a total of 13 km if it travels east for 5 km first.
Maths-
A greenhouse owner purchases fertilizer in 60-gallon drums. The fertilizer is mixed with water to make several batches of solution. Each batch of solution is made by mixing 3 quarts of fertilizer with water. What is the maximum number of batches of solution that can be made from one 60 -gallon drum of fertilizer? (1 gallon = 4 quarts)
A greenhouse owner purchases fertilizer in 60-gallon drums. The fertilizer is mixed with water to make several batches of solution. Each batch of solution is made by mixing 3 quarts of fertilizer with water. What is the maximum number of batches of solution that can be made from one 60 -gallon drum of fertilizer? (1 gallon = 4 quarts)
Maths-General
Maths-
A cable company recorded the percentage of households in the United States that had cable television from 1987 to 1997. In the scatterplot below, x represents the number of years since 1987 and y represents the percentage of households with cable television. The line of best fit for the data is shown.
Which of the following is the best interpretation of the slope of the line of best fit shown for these data?
A cable company recorded the percentage of households in the United States that had cable television from 1987 to 1997. In the scatterplot below, x represents the number of years since 1987 and y represents the percentage of households with cable television. The line of best fit for the data is shown.
Which of the following is the best interpretation of the slope of the line of best fit shown for these data?
Maths-General
Maths-
A cable company recorded the percentage of households in the United States that had cable television from 1987 to 1997. In the scatterplot below, x represents the number of years since 1987 and y represents the percentage of households with cable television. The line of best fit for the data is shown.
Which of the following is closest to the equation of the line of best fit shown?
A cable company recorded the percentage of households in the United States that had cable television from 1987 to 1997. In the scatterplot below, x represents the number of years since 1987 and y represents the percentage of households with cable television. The line of best fit for the data is shown.
Which of the following is closest to the equation of the line of best fit shown?
Maths-General
Maths-
If x4 - y4 = -15 and x2 - y2 = -3, what is the value of x2 + y2 ?
If x4 - y4 = -15 and x2 - y2 = -3, what is the value of x2 + y2 ?
Maths-General
Maths-
Kate bought a bus pass that had an initial value of $ 90. For every bus ride Kate takes, $ 1.80, the cost of one bus ride, is subtracted from the value of the pass. What percent of the initial value of Kate's bus pass is the cost of one bus ride?
Kate bought a bus pass that had an initial value of $ 90. For every bus ride Kate takes, $ 1.80, the cost of one bus ride, is subtracted from the value of the pass. What percent of the initial value of Kate's bus pass is the cost of one bus ride?
Maths-General
Maths-
At a snack bar, each medium drink costs $1.85 and each large drink costs c more dollars than a medium drink. If 5 medium drinks and 5 large drinks cost a total of $20.50, what is the value of c ?
At a snack bar, each medium drink costs $1.85 and each large drink costs c more dollars than a medium drink. If 5 medium drinks and 5 large drinks cost a total of $20.50, what is the value of c ?
Maths-General
Maths-
A pool initially contains 1,385 cubic feet of water. A pump begins emptying the water at a constant rate of 20 cubic feet per minute. Which of the following functions best approximates the volume v(t), in cubic feet, of water in the pool t minutes after pumping begins, for 0 ≤ t ≤ 69 ?
A pool initially contains 1,385 cubic feet of water. A pump begins emptying the water at a constant rate of 20 cubic feet per minute. Which of the following functions best approximates the volume v(t), in cubic feet, of water in the pool t minutes after pumping begins, for 0 ≤ t ≤ 69 ?
Maths-General
Maths-
Which of the following polynomials is equivalent to the expression above?
Which of the following polynomials is equivalent to the expression above?
Maths-General
