Question
One of the diagonal of a rectangle is 20 cm. If the difference between its length and width is 4 cm, then find the area of the rectangle.
Hint:
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2
The correct answer is: the area of the rectangle is 192 cm2
Let’ say the length of the rectangle is l and the width is w
It is given that the difference between the length and width is 4 cm. So
l - w = 4 cm
l = w + 4 ……….(1)
Given, length of diagonal(d) = 20 cm
Using Pythagoras theorem
d2 = b2 + l2
From equation (1)
202 = w2 + (w+4)2
400 = w2 + w2 + 16 + 8w
2w2 + 8w - 384 = 0
w2 + 4w - 192 = 0
Using quadratic formula
w = 
a = 1, b = 4, c = - 192
w = 
w = 
w = 
= 
= 12 cm
From equation (1)
l = 12 + 4 = 16 cm
Area of rectangle = Length × width = 12 × 16 = 192 cm2
Final Answer:
Hence, the area of the rectangle is 192 cm2.
Given, length of diagonal(d) = 20 cm
Using Pythagoras theorem
From equation (1)
Using quadratic formula
= = 12 cmFrom equation (1)
Area of rectangle = Length × width = 12 × 16 = 192 cm2
Final Answer:
Hence, the area of the rectangle is 192 cm2.
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