Question

A sign in the shape of a right triangle has one leg that is 28(inches) longer than the other leg. What is the length of the shorter leg of the perimeter is 120 inches ?

Answer 1

Explanation:

given that a sign in the shape of a right triangle has one leg that is 28(inches) longer than the other leg.

the perimeter is 120 inches

Let the shorter leg have length x inches Then the other leg has length as x+28 inches

The hypotenuse = 120- length of two legs together

=
`92-2x`

Since right angled triangle Pythagorean theorem is satisfied

i.e.

`x^2+(x+28)^2 = (92-2x)^2\\2x^2 +56x+784 =8464-368x+4x^2 \\2x^2-424x-7660=0\\x^2-212x-3830 =0\\`

We get x as negative or 228.744

this is not possible as perimeter is 120 inches only

Hence no solution