Question

Find the missing side lengths, put answer as radical in simplest form

Look at picture for reference

Answer 1

In a 30°-60°-90° right triangle, the length of the shorter leg is one-half the length of the hypotenuse, and the length of the longer leg is √3 times the length of the shorter leg. Here, the length of the shorter leg is (7/2)√10, so the length of the longer leg is (7/2)√30.

This length is the hypotenuse of the isosceles right triangle. The hypotenuse of an isosceles right triangle is √2 times the length of a leg, so x = (7/2)√15.