Consider a rectangle with a diagonal drawn between two vertices. Two right triangles are formed, each with one leg #5# inches longer than the other. The diagonal measure #25# inches. What do the legs measure?

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Answer 1 · 2016-10-13T02:35:38

Since a rectangle is a two dimensional shape with four right angles, we can apply pythagorean theorem.

Let #x# be the length of the shorter leg and #x + 5# be the length of the longer leg.

#x^2 + (x + 5)^2 = 25^2#

#x^2 + x^2 + 10x + 25 = 625#

#2x^2 + 10x - 600 = 0#

#2(x^2 + 5x - 300) = 0#

#x = (-5 +- sqrt(5^2 - 4 xx 1 xx -300))/(2 xx 1)#

#x = (-5 +- 35)/2#

#x = 30/2 and -40/2#

#x = 15 and -20#

A negative answer for a leg of a triangle is not possible, so the legs measure #15# and #20# inches.

Hopefully this helps!