The hypotenuse of a right triangle is 52 in. One leg of the triangle is 8 in. more than twice the length of the other. What is t
he perimeter of the triangle?
2 answers:
<span>c=52, a=2b+8
a^2+b^2=c^2
(2b+8)^2+b^2=52^2
4b^2+32b+64+b^2=2704
5b^2+32b-2640=0 see below
b=20, a=48
48+20+52
=120"</span>
Answer: 120 in.
Step-by-step explanation:
Given: The hypotenuse of a right triangle is 52 in.
Let the length of one leg be x, then the length of other leg will be 2x+8
By Pythagoras theorem of right triangle, we have
![52^2=x^2+(2x+8)^2\\\\\Rightarrow\ 2704=x^2+4x^2+32x+64\\\\\Rightarrow\ 2704=5x^2+32x+64\\\\\Rightarrow\5x^2+32x-2640=0\\\\\Rightarrow\ (x-20)(5x+132)\\\\\Rightarrow\ x=20\ or\ x=\dfrac{-132}{5}\ \ \ \text{[side cannot be negative]}\\\\\Rightarrow\ x=20](https://tex.z-dn.net/?f=52%5E2%3Dx%5E2%2B%282x%2B8%29%5E2%5C%5C%5C%5C%5CRightarrow%5C%202704%3Dx%5E2%2B4x%5E2%2B32x%2B64%5C%5C%5C%5C%5CRightarrow%5C%202704%3D5x%5E2%2B32x%2B64%5C%5C%5C%5C%5CRightarrow%5C5x%5E2%2B32x-2640%3D0%5C%5C%5C%5C%5CRightarrow%5C%20%28x-20%29%285x%2B132%29%5C%5C%5C%5C%5CRightarrow%5C%20x%3D20%5C%20or%5C%20x%3D%5Cdfrac%7B-132%7D%7B5%7D%5C%20%5C%20%5C%20%5Ctext%7B%5Bside%20cannot%20be%20negative%5D%7D%5C%5C%5C%5C%5CRightarrow%5C%20x%3D20)
Perimeter of triangle will be:

- Pythagoras theorem of right triangle says that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
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