The hypotenuse of a right triangle is 53 units long. Find the other two sides if the perimeter of the triangle is 126 units.

Question

The hypotenuse of a right triangle is 53 units long. Find the other two sides if the perimeter of the triangle is 126 units. 

Answer 1

Perimeter = 126 = sum of the 3 sides = 53 + x + y

126-53 = x+y

73 = x+y

y = 73-x

hypotenuse squared = sum of squares of the other 2 sides

53^2 = x^2 +y^2

2809 = x^2 + (73-x)^2

2809 = x^2 + 5329 -146x + x^2

5329 -2809 = -2x^2 +146x

2x^2 -146x +2520 = 0

x^2 - 73x + 1260 = 0

use the quadratic formula or factor

(x-45)(x+28) = 0

x = -28 or 45

x=45

y = 126-53-45 = 126-98 = 28

y = 28

the other two sides are 28 and 45

or use the quadratic formula

x= 73/2 +or - (1/2)sqr(73^2 -4(1260)

x = 73/2 + (1/2)17

x = 73/2 + or - 17/2

x = 90/2 or 56/2

x = 45 or 28

the other two sides of the right triangle are 28 and 45

check the answer, with the Pythagorean Theorem

hypotenuse squared = sum of squares of the other two sides.

28^2 + 45^2 = 53^2

784 + 2025 = 2809

2809 = 2809