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 $=48$ .

The legs of a right triangle have lengths x+2x+2 and x +6 x +6. The hypotenuse has length 2x2x. What is the perimeter of the triangle?