Question 1120240
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Triangles XPY and XYW are similar, because they are both right triangles that share angle X.  So<br>
PX/XY = XY/WX
(XY)^2 = PX*WX = 14*32 = 448
XY = sqrt(448) = 8*sqrt(7)<br>
Then from the Pythagorean Theorem in triangle XPY, YP = 6*sqrt(7).<br>
Answers...<br>
(I) YQ = XY-XQ = 6*sqrt(7)-9.8
(II) the area of triangle XPY is (1/2)(PX)(PY) = (1/2)(14)(6*sqrt(7) = 42*sqrt(7)