MathDB
AHSME 1950- part 3

Source:

July 20, 2008
geometryrectangleratio

Problem Statement

A rectangle inscribed in a triangle has its base coinciding with the base bb of the triangle. If the altitude of the triangle is hh, and the altitude xx of the rectangle is half the base of the rectangle, then:
<spanclass=′latex−bold′>(A)</span> x=12h<spanclass=′latex−bold′>(B)</span> x=bhb+h<spanclass=′latex−bold′>(C)</span> x=bh2h+b<spanclass=′latex−bold′>(D)</span> x=hb2<spanclass=′latex−bold′>(E)</span> x=12b<span class='latex-bold'>(A)</span>\ x=\dfrac{1}{2}h \qquad <span class='latex-bold'>(B)</span>\ x=\dfrac{bh}{b+h} \qquad <span class='latex-bold'>(C)</span>\ x=\dfrac{bh}{2h+b} \qquad <span class='latex-bold'>(D)</span>\ x=\sqrt{\dfrac{hb}{2}} \qquad <span class='latex-bold'>(E)</span>\ x=\dfrac{1}{2}b
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