Question

The hypotenuse of the right triangle is 5y inches long. The lengths of the legs are x + 8 and x + 3 inches. If the perimeter of the triangle is 60 inches and the length of the hypotenuse minus the length of the shorter leg is 10 inches, how many inches long is the hypotenuse?

Answer 1

Answer:

25

Step-by-step explanation:

The perimeter of triangle is equal to the sum of all sides of triangle

then:

5y + (x+8) + (x+3) = 60

5y + 2x +11 = 60

5y +2x = 49  ..............................................................(1)

the hypotenuse - shorter leg = 10

hint (  shorter leg ) = x+3

then

5y - (x + 3 ) = 10

5y - x - 3 = 10

5y - x = 13               .................................................... (2)

from 1 and 2

5y +2x = 49  .................................................................. (3)

5y - x = 13 (multiply both sides by 2 )

10y - 2x = 26 ..................................................................(4)

by sum 3 and 4

15y = 75

then y = 75/15 = 5

then hypotenuse = 5y = 5 x 5 = 25