Question

The hypotenuse of a right triangle is 1inch
longer than the longer leg The shorter leg is
7 inches shorter than
the longer teg. Find the
length of the hypo tenuse.​

Answer 1

Answer:

Longer leg = x

Shorter leg = x - 7

Hypotenuse = 1 + x

x^2 + (x - 7)^2 = (1 + x)^2

x^2 + x^2 - 14x + 49 = 1 + 2x + x^2

Collect like terms:

x^2 - 16x + 48 = 0

(x - 4)(x - 12) = 0

x - 4 = 0

x = 4 (no answer as shorter leg = - number)

x - 12 = 0

x = 12

Longer leg = 12 inches

Shorter leg = 5 inches

Hypotenuse = 13 inches.

Hope this helps.