The hypoenuse of a right triangle is 10 m long. The shorter leg is 2 m shorter than the longer leg. Find the side lengths of the triangle.

A2+b2=c2

x2 + (x-2) 2=102

x2+x2-4x+4=100

2x2-4x+4-100=0

2x2-4x-96=0

divide both sides by 2

x2-2x-48=0

factor

(x-8) (x+6) = 0

x-8=0

x=8 inches

x-2=6 inches

x and x-2 are the legs and the hypotenuse is 10 inches

something I noticed ...

are you familiar with a 3-4-5 right triangle?

32+42=52, 9+16=25

if you double or triple or quadruple, or ... you get another right triangle

6,8,10 is a right triangle, 9,12,15 is a right triangle, etc

look at the 6-8-10 right triangle; the hypotenuse is 10 and one leg is 2 less than the other-exactly what was stated in the problem