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)