Question

Hello!

I've been trying to solve this for a little bit, although I don't understand how to start.

Question: Solve for x and y.
Image: Attached

Answer 1

`x=12√(6)\ units\\ \\y=12√(2)\ units`

Explanation:

In a right triangle, the height drawn to the hypotenuse is geometric mean between the measures of the two segments of the hypotenuse, so

`y^2=24\cdot 12\\ \\y^2=2\cdot 12\cdot 12\\ \\y=√(2\cdot 12\cdot 12)\\ \\y=12√(2)\ units`

If the height is drawn to the hypotenuse in a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg. So

`x^2=24\cdot (24+12)\\ \\x^2=24\cdot 36\\ \\x^2=4\cdot 6\cdot 36\\ \\x=√(4\cdot 6\cdot 36)\\ \\=x=2\cdot 6√(6)\\ \\x=12√(6)\ units`