Question

The shorter leg of the right triangle is 8 less than the hypotenuse. The longer leg is 1 less than the hypotenuse. Find the perimeter of the triangle.

Answer 1

hypotenuse = h
leg1 = h-8
leg2 = h-1

h² -(h-8)² = (h-1)²

h² - [h² -16h +64] = h² -2h +1
16h -64 = h² -2h +1
h² -18h + 65 = 0

hypotenuse = 13
leg1 = 13-8 = 5
leg2 = 13-1 =12

Perimeter = 13 + 5 + 12 = 30

Answer 2

The perimeter of the triangle is 30 and this can be determined by using the Pythagorean theorem and also by using the formula of the perimeter.

Given :

• The shorter leg of the right triangle is 8 less than the hypotenuse.
• The longer leg is 1 less than the hypotenuse.

Let the hypotenuse be 'H' then the shorter leg of the right triangle is (H - 8) and the longer leg is (H - 1).

Applying Pythagorean theorem in the given right triangle.

$\rm H^2=(H-1)^2+(H-8)^2$

Simplify the above equation in order to determine the value of 'H'.

$\rm H^2=H^2+1-2H+H^2+64-16H$

$\rm H^2-18H+65=0$

Factorize the above equation.

$\rm H^2-13H-5H+65=0$

H(H - 13) - 5(H - 13) = 0

(H - 13)(H - 5) = 0

So, the hypotenuse is 13, the shorter leg is 5 and the longer leg is 12.

The perimeter of the triangle is given by:

P = 13 + 12 + 5

P = 30

For more information, refer to the link given below:

https://brainly.com/question/3382480