Answer:
remember the Pythagorean theorem: a^2 + b^2 = c^2 so c = sqrt(a^2 + b^2)
21: We split it into three parts, the 2 sides of the triangle, and the side of the rectangle. For the rectangle, we know it's 10 from the other side. Since the two triangles are both right-angle triangles, we use the Pythagorean theorem.
15^2 - 12^2 = 9^2, so our side length for both triangles is 9.
9 + 9 + 10 = 28 = x
22: We want to draw a right-angle triangle so that we can use the Pythagorean theorem. The vertical side would be 8, and the horizontal side would be 11-5 = 6. 8^2 + 6^2 = 10^2, so x would be 10.
23: We would draw a right-angle triangle. Vertical side: 10-6 = 4 Hypotonuse: 12. So 12^2 - 4^2 = 128, so x = 8
which is the sqrt of 128.
24: We would need to solve for the height which would be 10^2 - 6^2 = 8^2. So the height would be 8. Then, 8^2 + 15^2 = x^2 = 17^2. So x would be 17.