SOLUTION: An isosceles right triangle has an area of 98 square units, what is the perimeter?

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Question 288845: An isosceles right triangle has an area of 98 square units, what is the perimeter?
Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the length of the common leg. Then both the base and the height of the triangle are x so the area is:
1/2*base*height = 98
(1/2)*x*x = 98
x^2/2 = 98
x^2 = 2*98
x^2 = 196
x = 14
Let h be the hypotenuse. Then, by the Pythagorean Theorem, we have;
h^2 = x^2 + x^2
h^2 = 2*(x^2)
h = x*sqrt(2)
h = 14*sqrt(2)
The perimeter then is x + x + h = 14 + 14 + 14*sqrt(2) = 14*(2 + sqrt(2))