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.

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(52790) (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,


     +  = ,   or


     = 169

     = 0

     = 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.    +  = 144 + 25 = 169 = .    ! Correct !

Solved.

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

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