In a right tiangle, the length of one leg is two more than the other leg. If the length of the hypotenuse is √(52) , find the length of the two legs?

Question

SOLVING PROBLEMS INVOLVING QUADRATIC EQUATIONS AND RATIONAL ALGEBRAIC EQUATIONS

Answer 1

h=2+b h=height, b = base

square of the hypotenuse = sum of squares of the other 2 sides

52 = h^2 + (h-2)^2 = h^2 + h^2 -4h + 4 = 2h^2 - 4h + 4

2h^2 - 4h - 48 = 0 divide by 2

h^2 -2h -24 =0

(h-6)(h+4) = 0

h= 6, b =4

sides are 6 and 4

hypotenuse= sqr(4^2 + 6^2) = sqr(16+36) = sq52