An isosceles right triangle has a hypotenuse of length e. Select all that are true for the triangle.

Note: if the formulas don't load properly, then you may need to refresh the page.

======================================================

Explanation:

For any 45-45-90 right triangle, the hypotenuse H is always sqrt(2) times the leg L

In terms of symbols, we can say

We're told the hypotenuse is e, so H = e

Let's solve for L in terms of e

Now let's multiply top and bottom by to rationalize the denominator

If the hypotenuse is e, then the length of each leg is

This matches with choice C, which is one of the two answers. This allows us to rule out choices A and B, as those expressions are not equivalent to the expression for choice C.

----------------

The two legs of any right triangle form the base and height. The order doesn't matter. The base is always perpendicular to the height. In a right triangle, the two legs are always perpendicular.

The base and height are each.

The area of the triangle is...

This matches with choice E, which is the other answer. Choices D and F are eliminated as they are not equivalent to the expression for choice E.

i can't see the picture : /