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

Question 309830: The legs of a right triangle have lengths x+2 and x+6. The hypotenuse has a length 2x. What is the perimeter
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The legs of a right triangle have lengths x+2 and x+6.
The hypotenuse has a length 2x.
What is the perimeter.
:
P = (x+2) + (x+6) + 2x
P = 4x + 8
:
Find x using the a^2 + b^2 = c^2
(x+2)^2 + (x+6)^2 = (2x)^2
FOIL
x^2 + 4x + 4 + x^2 + 12x + 36 = 4x^2
Combine like terms
x^2 + x^2 - 4x^2 + 4x + 12x + 40 = 0
:
-2x^2 + 16x + 40 = 0
Simplify change the signs, divide by -2
x^2 - 8x - 20 = 0
Factor this to
(x-10)(x+2) = 0
positive solution is what we want here
x = 10
:
P = 4x + 8
P = 4(10) = 8
P = 48 is the perimeter
:
:
Check solution using 10 for x
leg 1: 10 + 2 = 12
leg 2: 10 + 6 = 16
hypot: 2(10) = 20
-------------------
perimeter is: 48
RELATED QUESTIONS
the legs of a right triangle have lengths x+2 and x+6. The hypotenuse has the length 2x.... (answered by mananth)

The legs of a right triangle have lengths x + 2 and x + 6. the hypotenuse has length 2x.... (answered by themathtutor2009)

The legs of a right triangle have lengths (in units) x+2 and x+6. The hypotenuse has... (answered by stanbon)

I need your help on this question concerning triangles: The legs of a triangle have... (answered by stanbon)

The legs of a right triangle have lengths (in units) x+2 and x+6. The hypotenuse has... (answered by richwmiller)

the legs of a right triangle have lengths x+4 and x+7. The hypotenuse has length 3x. Find (answered by robertb)

A right triangle has legs of 5 and x+2 and a hypotenuse of length x+3. What is the... (answered by acalgebra,Alan3354)

11. A right triangle has legs with lengths x units and 7 units. The hypotenuse has length (answered by josmiceli)

A right triangle has legs with lengths x units and 7 units. The hypotenuse has length x+1 (answered by solver91311)