Let, one leg be x units. since the other leg is 9.0 units shorter than the other, the measure of the other leg =x-9 hypotenuse =13.0 units According to Pythagorean theorem, the square of the hypotenuse is equal to the sum of squares of the other two sides. x^2 +(x-9)^2 =13^2 x^2 + x^2 -18x +81 = 169 2x^2-18x-88=0 Divide the whole equation by 2 x^2 - 9x -44 =0 Let's use the quadratic formula to find the roots. formula: x= [-b ± sqrt(b^2-4*a*c)]/2*a a=1 b=-9 c=-44 x= [9±sqrt(81+176)]/2 =[9±sqrt(257)]/2 =[9±16.03]/2 =25.03/2 or -7.03/2 length of a triangle cannot be negative, Therefore, x=25.03/2 =12.52 one leg =12.5 units other leg =12.52-9 =3.5 units
