SOLUTION: the hypotenuse of a right triangle is 13 cm long. The shorter leg is 7cm shorter than the longer leg. Find the side lengths of the triangle.

Algebra ->  Test -> SOLUTION: the hypotenuse of a right triangle is 13 cm long. The shorter leg is 7cm shorter than the longer leg. Find the side lengths of the triangle.       Log On


   

Question 1138304: the hypotenuse of a right triangle is 13 cm long. The shorter leg is 7cm
shorter than the longer leg. Find the side lengths of the triangle.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the longer leg.

Then the shorter leg is (x-7) centimeters long.


According to the Pythagorean theorem,


    x%5E2 + %28x-7%29%5E2 = 13%5E2,   or


    x%5E2+%2B+x%5E2+-+14x+%2B+49 = 169

    2x%5E2+-+14x+-+120 = 0

    x%5E2+-+7x+%2B+60 = 0


Factor the quadratic polynomial

    (x-12)*(x+5) = 0.


Its roots are x= 12 and  x= -5,  but only positive solution is meaningful.


ANSWER.  The longer leg is 12 cm;  the shorter leg is  12-7 = 5 cm.


CHECK.   12%5E2 + 5%5E2 = 144 + 25 = 169 = 13%5E2.    ! Correct !

Solved.

(5,12,13) is the classic Pythagorean right angled triangle.