The legs of a right triangle have lengths #x+2# and# x +6#. The hypotenuse has length #2x#. What is the perimeter of the triangle?

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Answer 1 · 2018-01-08T00:05:19

The perimeter is #48#. Note this is a constant, not depending on #x#. We can solve for #x#, see below.

Legs=#x+2, x+6#

Hypoteneuse=#2x#

Then

#(x+2)^2+(x+6)^2=(2x)^2#

#(x^2+4x+4)+(x^2+12x+36)=4x^2#

#2x^2-16x-40=0#

#2(x+2)(x-10)=0#

The sides of the triangle must be positive so #color(blue)(x=10)#.

Then the legs are #12# and #16#, the hypoteneuse is #20# (check that #12^2+16^2=20^2#), and their sum is the perimeter#=48#.