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x=√14

Step-by-step explanation:

Hi there!

We are given a right triangle (notice the right angle), with acute angles measuring 45° and 45°, the hypotenuse (the side opposite from the right angle) labeled as x, and one of the legs (one of the sides that makes up the right angle) labeled as √7

As these two angles are the same measure, the triangle is isosceles.

So that means that the measure of the other leg (the unmarked side) is also √7.

This triangle is a special type of triangle; a 45°-45°-90° triangle. For this triangle, if the length of the legs are a, then the hypotenuse has the length  a√2

In this case, √7 is a, and as x is the measure of the hypotenuse, it must be equal to a√2, which substituting the values of a would get √7 * √2, which is √14.

The radical cannot be simplified further, so √14 is the answer.

Hope this helps!

step-by-step explanation: