What is the length of the shorter leg of a right triangle if the longer leg is 12 feet more than the shorter leg and the hypotenuse is 12 feet less than twice the shorter leg?

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Answer 1 · 2018-04-22T03:22:33

#s=36 " un"#

We will use the variables:
#s# for shorter leg
#l# for the longer leg
#h# for hypotenuse

We have:
#l=s+12#
#h= 2s-12#

Knowing this is a right triangle:
#s^2+l^2= h^2#

Let's substitute the above given equations for #h# and #l#:
#s^2+(s+12)^2= (2s-12)^2#

Simplify:
#s^2+s^2+24s+144=4s^2-48s+144#

Set the expression equal to #0#:
#2s^2-72s=0#

Factor with GCF:
#2s(s-36)=0#

#s=0# distance of the leg can't be zero
#s=36 un#

Answer 2 · 2018-04-22T03:44:41

Using the Pythagorean Theorem, we find that the length of the shorter side is 36 feet.

Let's call all shorter leg #s#.

#s^2 = (2s - 12)^2 - (s + 12)^2#

#color(green)(s = 36)#