#1**+2 **

Call the intersection of PR and SQ = O

Triangle SOR similar to triangle YOX

XY / SR = 5 / 28

Then the height of triangle YOX is 5/28 of the height of triangle SOR

Then we can divide half of the height of the trapezoid into 33 equal parts

Height of triangle SOR is 28 of these parts and height of triangle YOX is 5 of them

And triangle QOP is similar to triangle SOR

So.....the height of triangle QOP = 33 + 5 = 38 equal parts of the total height of the trapezoid

So, since the trangles are similar → PQ / SR = 38 / 28

So PQ = (38/28) SR = (38/28) * 28 = 38

CPhill Mar 20, 2024