Problem: The base of a triangle is of length b​, and the altitude is of length h​. A rectangle of height x​ is inscribed in the triangle with the base of the rectangle in the base of the triangle. The area of the rectangle is:
Answer Choices:
A. hbx​(h−x)
B. bhx​(b−x)
C. hbx​(h−2x)
D. x(b−x)
E. x(h−x)
Solution:
Designate the base of the rectangle by y​. Then, because of similar triangles, yh−x​=bh​,y=hb​(h−x)
∴ Area =xy=hbx​(h−x)