# SOLUTION: one leg of a right triangle is 6cm shorter than the other leg. the length of the hypotenuse is 30cm. find the length of the longer leg.

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 Question 283712: one leg of a right triangle is 6cm shorter than the other leg. the length of the hypotenuse is 30cm. find the length of the longer leg.Answer by stanbon(57282)   (Show Source): You can put this solution on YOUR website!one leg of a right triangle is 6cm shorter than the other leg. the length of the hypotenuse is 30cm. find the length of the longer leg. --------------------- one leg: x other leg: x-6 hyp = 30 ---------------------------------- Pythagoras: x^2 + (x-6)^2 = 30^2 x^2 + x^2-12x+36 = 900 2x^2 -12x - 864 = 0 x^2 - 6x - 432 = 0 (x+18)(x-24) = 0 Positive solution: x = 24 cm (one leg) x-6 = 18 cm (other leg) ========================= Cheers, Stan H.