Question

The hypotenuse of a right triangle is 5 inches long. The shorter leg is 1 inch shorter than the longer leg. Find the side lengths of the triangle.

Answer 1

Okay, well for a right triangle with legs a and b and hypotenuse c we have:
a2+b2= c2

since we know the hypotenuse (c), we have:
a2+b2= 25
since the short leg is 1 inch shorter than the longer leg,
we can say that a = b-1
So now we have:
(b-1)2+ b2 = 25
b2 - 2b +1 +b2 = 25
2b2-2b -24 = 0
2(b2-b-12) = 0

b2-b-12 = 0
(b-4)(b+3) = 0
Because you can't have a negative length, b = 4
If b = 4, then a = 4-1 = 3
So,
b=4
a=3