Question 837682
this is an isosceles right triangle.
the legs are of equal length.
the length of 1 leg is equal to x + 2.
in a right triangle, a^2 + b^2 = c^2
let a = x + 2
let b = x + 2
let c = 12
the formula becomes:
(x+2)^2 + (x+2)^2 = 12^2
this can be simplified to:
2 * (x+2)^2 = 144 which can be further simplified to:
(x+2)^2 = 72
take the square root of both sides of this equation to get:
sqrt((x+2)^2) = sqrt(72)
simplify to get:
x+2 = +/- sqrt(72)
subtract 2 from both sides of this equation to get:
x = -2 +/- sqrt(72)
you get 2 possible values of x.
they are:
x = -10.48528137 or:
x = 6.485281374


since x can't be negative, the only possible solution is x = 6.485281374.
this means that (x+2) is equal to 8.485281374
to confirm this solution is good, 2 * (8.485281374)^2 to see what it gets you.
it gets you 144 which is the hypotenuse squared, as it should, so the solution is good.
each leg of the triangle is equal to 8.485281374 and the hypotenuse is equal to 12.
the perimeters is equal to 2 * the legs plus the hypotenuse which makes the perimeter of the triangle equal to 28.97056275 cm  which you can round as much as you like.