Question

Two legs of a right triangle are two consecutive even integers while the hypotenuse is 10 inches. What are the measure of both legs?

Answer 1

6 inches and 8 inches

Explanation:

We know that `a^2 + b^2 = c^2`
Let `a=x`, `b=x+2`, `c=10`
`x^2 + (x+2)^2 = 10^2`
`x^2+x^2+4x+4=100`
`2x^2+4x+4=100`
`x^2+2x+2=50`
`x^2+2x-48=0`
`(x-6)(x+8)=0`
`x=6 or x=-8`
`x=6` (can't be negative)
`x+2=8`
`a=6, b=8`