A right triangle has one leg that is 8 inches shorter than the other leg, the hypotenuse is 30 inches long, how do you find the length of each leg?

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Answer 1 · 2017-06-03T17:03:43

The legs are #24.83 and 16.83# inches long.

The lengths of the two short sides (the legs of the right-angle) are:

#x and (x-8)# inches

The length of the hypotenuse is #30# inches

Write an equation using Pythagoras' Theorem:

#x^2 + (x-8)^2 = 30^2#

#x^2 +x^2 -16x +64 = 900" "larr# make =0

#2x^2 -16x -836 =0" "larr div 2#

#x^2 -8x-418 =0" "larr# does not factorise

Solve for #x# by completing the square method:

#x^2 -8x +16 = 418+16#

#(x-4)^2 = 434#

#x -4 =+-sqrt434" "larr# ignore the negative root.

#x = sqrt434+4#

#x = 24.83#

The legs are #24.83 and 16.83# inches long.

Check:

#sqrt(24.83^2 +16.83^2) = 30#