MathDB

37

Part of 1956 AMC 12/AHSME

Problems(1)

Estate on a Map

Source:

2/15/2009
On a map whose scale is 400 400 miles to an inch and a half, a certain estate is represented by a rhombus having a 60∘ 60^{\circ} angle. The diagonal opposite 60∘ 60^{\circ} is 316 \frac {3}{16} in. The area of the estate in square miles is: <spanclass=′latex−bold′>(A)</span> 25003<spanclass=′latex−bold′>(B)</span> 12503<spanclass=′latex−bold′>(C)</span> 1250<spanclass=′latex−bold′>(D)</span> 562532<spanclass=′latex−bold′>(E)</span> 12503 <span class='latex-bold'>(A)</span>\ \frac {2500}{\sqrt {3}} \qquad<span class='latex-bold'>(B)</span>\ \frac {1250}{\sqrt {3}} \qquad<span class='latex-bold'>(C)</span>\ 1250 \qquad<span class='latex-bold'>(D)</span>\ \frac {5625\sqrt {3}}{2} \qquad<span class='latex-bold'>(E)</span>\ 1250\sqrt {3}
geometryrhombus