SOLUTION: an isosceles right-angled triangle has one side length of (x+2) cm and the length of the hypotenuse is 12 cm. find the perimeter of the triangle?

Question 837682: an isosceles right-angled triangle has one side length of (x+2) cm and the length of the hypotenuse is 12 cm. find the perimeter of the triangle?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

RELATED QUESTIONS
an isosceles right angled triangle has one side length of (x+2) cm and the length of the... (answered by KMST)

A right angled triangle has one leg of 12 cm and a hypotenuse of 14 cm. Find the length... (answered by farohw)

The hypotenuse of an isosceles right triangle measures 16 cm. Find the length of a... (answered by ewatrrr)

Perimeter of right angled triangle is 30 cm and hypotenuse is 13 cm. Find the length of... (answered by DrBeeee)

the length of a side of a triangle are x cm,(x+1)cm and (x+2)cm.Determine x so that this... (answered by MathLover1)

If the square of the hypotenuse of an isosceles right triangle is 128 cm^2, find the... (answered by ikleyn)

Find the length of the hypotenuse of a right angled triangle with one leg 7 cm longer... (answered by stanbon,nerdybill,jojo14344)

A right isosceles triangle has equal sides of d cm and sqrt(12+d) cm. Find the length of... (answered by greenestamps,Alan3354)

2. The length of the hypotenuse of a right triangle is 13 cm. The length of one leg is... (answered by jim_thompson5910)