The shorter leg of a right triangle is 7ft shorter than the longer leg. The hypotenuse is 7ft longer than the longer leg. Find the side lengths of the trian

Question

The shorter leg of a right triangle is
7ft
shorter than the longer leg. The hypotenuse is
7ft
longer than the longer leg. Find the side lengths of the triangle.

Answer 1

n=longer leg

n-7=shorter leg

n+7=hypotenuse

using the Pythagorean Theorem...

(n+7)^2=n^2+(n-7)^2

n^2+14n+49=n^2+n^2-14n+49

n^2+14n+49=2n^2-14n+49

subtract 49 from both sides

n^2+14n=2n^2-14n

0=2n^2-14n-n^2-14n

0=n^2-28n

factor

n(n-28)=0

n-28=0

n=28 feet

n+7=35 feet

n-7=21 feet

the legs are 21 feet and 28 feet

the hypotenuse is 35 feet

this is basically a 3-4-5 right triangle

3(7), 4(7), 5(7)