The length of the longer leg of a right triangle is
13inches
more than three times the length of the shorter leg. The length of the hypotenuse is
14inches
more than three times the length of the shorter leg. Find the side lengths of the triangle.
a^2+b^2=c^2 (13+3b)^2+b^2=(14+3b)^2 9b^2+78b+169+b^2=9b^2+84b+196 10b^2+78b+169=9b^2+84b+196 minus 9b^2 both sides b^2+78b+169=84b+196 minus 84b both sides b^2-6b+169=196 minus 196 both sides b^2-6b-27=0 factor (b+3)(b-9)=0 set to zero b+3=0 b=-3, false, dimentions cannot be negative
