SOLUTION: if the length of the hypotenuse of a 30-60-90 triangle is 7 square root of 2 what's the area and perimeter. I have to find proofs for the problem for modern geometry class.

Question 801311: if the length of the hypotenuse of a 30-60-90 triangle is 7 square root of 2 what's the area and perimeter. I have to find proofs for the problem for modern geometry class.
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Draw the triangle. This is half of an equilateral triangle. The hypotenuse of the 30-60-90 triangle is two times the short leg.

Let y=height
Let x=short leg
Already known, , hypotenuse, same as side of equilateral triangle.

As property of 30-60-90 triangle, .
According to pythagorean theorem,
We already know h, so we want to use the h relationship formula to make equation with only one unknown variable in the pythagorean theorem relationship.
, so substitute:

Now go back and find . You will find area as which is simply .
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