SOLUTION: If the area of a right isosceles triangle is 4, how long are its sides?

Question 697336: If the area of a right isosceles triangle is 4, how long are its sides?
Answer by Positive_EV(69) (Show Source): You can put this solution on YOUR website!
The area of a triangle is equal to (1/2)*base*height. For a right triangle, the base and the height are the legs.
Since this is an isosceles triangle, both legs are the same length. Let L = the length of a leg:
- divide both sides by 1/2:
- take the square root of both sides:
.
The legs are both . For the hypotenuse, you can use the Pythagorean theorem:
, where :

, take the square root of both sides:

The legs of the right triangle are , and the hypotenuse is 4.
Follow-up edit: In this particular case, there are other ways to find the third side given the legs. Since this is a right isosceles (45-45-90) triangle, the ratios of the sides are going to be 1:1:.
So, another way to find the hypotenuse is to multiply the length of a leg by , which will also give 4 for the hypotenuse.
This specific method only works for right isosceles triangles, though. There's one other special case like this -- if you know the angles are 30, 60, and 90 degrees, the ratios of the sides are 1::2. The Pythagorean theorem works on any right triangle -- if you know any two sides you can always find the third side of a right triangle with it.
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