Question
The perimeter of △ 𝐻𝐺𝐹 must be between what two integers? Explain your reasoning
The correct answer is: Hence, perimeter is between 4 and 24.
Answer:
- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c
b < a + c
c < a + b
- while finding possible lengths of third side use below formula
difference of two side < third side < sum of two sides
- Step-by-step explanation:
- Given:
GJ = 3 units
JH = 4 units
FJ = 5 units
- Step 1:
- Find length of third side in GJH.
- In △GJH,
GJ = 3 and JH = 4
According to triangle inequality theorem,
difference of two side < third side < sum of two sides
b – a < c < a + b
4 – 3 < c < 4 + 3
1 < c < 7
Hence, 1 < GH < 7.
Step 2:
- Find length of third side in △FJH.
- In △FJH,
FJ = 5 and GJ = 3
According to triangle inequality theorem,
difference of two side < third side < sum of two sides
b – a < c < a + b
5 – 3 < c < 5 + 3
2 < c < 8
Hence, 2 < FH < 8.
Step 3:
- Find length of third side in △FJG.
- In △FJG,
FJ = 5 and JH = 4
According to triangle inequality theorem,
difference of two side < third side < sum of two sides
b – a < c < a + b
5 – 4 < c < 5 + 4
1 < c < 9
Hence, 1 < FG < 9.
Step 3
Find perimeter of △HGF
Perimeter = HF + JH + GF
Hence,
1 + 1 + 2 < HF + JH + GF < 7 + 8 + 9
4 < HF + JH + GF < 24
- Final Answer:
Hence, perimeter is between 4 and 24.
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c
- while finding possible lengths of third side use below formula
- Given:
- Step 1:
- Find length of third side in GJH.
- In △GJH,
According to triangle inequality theorem,
difference of two side < third side < sum of two sides
Hence, 1 < GH < 7.
Step 2:
Hence, 2 < FH < 8.
Step 3:
Hence, 1 < FG < 9.
Step 3
Find perimeter of △HGF
Perimeter = HF + JH + GF
Hence,
Related Questions to study
Choose the imperative, sentence
Choose the imperative, sentence
Your house is 2 miles from the library. The library is 34 miles from the grocery store. What do you know about the distance from your house to the grocery store? Explain. Include the special case when the three locations are all in a straight line.
Your house is 2 miles from the library. The library is 34 miles from the grocery store. What do you know about the distance from your house to the grocery store? Explain. Include the special case when the three locations are all in a straight line.
Choose the antonym for ‘respect’
Choose the antonym for ‘respect’
List the sides and the angles in order from smallest to largest
List the sides and the angles in order from smallest to largest
Explain whether this graph represents a function ?
In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function
Explain whether this graph represents a function ?
In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function
List the sides and the angles in order from smallest to largest.
List the sides and the angles in order from smallest to largest.
Choose the correct synonyms for "technical skill"?
Choose the correct synonyms for "technical skill"?
Choose the word that rhyme with 'easier'.
Choose the word that rhyme with 'easier'.
Use elimination to solve the system of equations.
For any equation of the form: 
, the solutions are: 
Use elimination to solve the system of equations.
For any equation of the form: , the solutions are:
Explain whether this graph represents a function ?
In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.
Explain whether this graph represents a function ?
In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.
