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
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perimeter is: 48
