For the right triangles below, find the exact values of the side lengths a and d. If necessary, write your responses in simplified radical form.

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Step-by-step explanation:

First one is half an equilateral triangle. It means the hypotenuse is twice the shorter side, so 2a. Then let's apply the Pythagorean theorem:

At this point is simply take the square root, use the positive value since they're lengths, and rearrange the fraction to have things look nice:

Second one is half a square - or if you prefer, it's an isosceles right triangle, both side lengths are 2. Then its Pythagoras again:

Again, we just have to pick the square roots, and rearrange in a better looking way.

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