SOLUTION: The hypotenuse of a right triangle is 3 cm longer than the longer leg. The shorter leg is 21 cm shorter than the longer leg. Find the length of the longer leg of the triangle.

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Question 1142615: The hypotenuse of a right triangle is 3 cm longer than the longer leg. The shorter leg is 21 cm shorter than the longer leg. Find the length of the longer leg of the triangle.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
x and y legs,
h hypotenuse,


Follow your problem description the way it is written. Also check if your result makes sense.
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
Let x be the length of the longer leg, in centimeters.


Then the shorter leg length is (x-21) cm, while the hypotenuse length is (x+3) cm.


The Pythagorean theorem gives you an equation


    x^2 + (x-21)^2 = (x+3)^2


Simplify and solve for x:


    x^2 + x^2 - 42x + 441 = x^2 + 6x + 9

    x^2 - 48x + 432 = 0

    (x-12)*(x-36) = 0


The roots of the last equation are 12 and 36.


But only greater of the two roots, namely 36, is the solution to the problem,

since 12 becomes NEGATIVE, when 21 is subtracted from it.


ANSWER.  The longer leg is 36 cm long.


CHECK.   36^2 + (36-21)^2 = 1521,  and  (36+3)^2 = 39^2 = 1521.    ! Correct !


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