The length of the hypotenuse of a right triangle is 13. The length of the shorter leg is 7 less than the length of the longer leg. What is the length of the shorter leg?

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Answer 1 · 2016-09-26T03:23:38

5

Let #x# be the length of the shorter leg

#=># the length of the longer leg is #x + 7#

By the Pythagorean Theorem, in a right triangle, the sum of the square of the legs is equal to the square of the hypotenuse

#a^2 + b^2 = c^2#

#x^2 + (x + 7)^2 = 13^2#

#=> x^2 + x^2 + 14x + 49 = 169#

#=> 2x^2 + 14x - 120 = 0#

#=> x^2 + 7x - 60 = 0#

#=> (x - 5)(x + 12) = 0#

#=> x = 5, x = -12#

However, since we are dealing with lengths, negative values are not possible. Hence #x = 5#