The diagram shows a smaller rectangle made from three squares, each of area 25 cm2 , inside a larger rectangle. Two of the vertices of the smaller rectangle lie on the mid-points of the shorter sides of the larger rectangle. The other two vertices of the smaller rectangle lie on the other two sides of the larger rectangle. What is the area, in cm2 , of the larger rectangle?
A. 125 B. 136 C. 149 D. 150 E. 172
D.
Join the vertices of the smaller rectangle that lie on the shorter sides of the larger rectangle, as shown in the diagram. This line splits the smaller rectangle into two congruent triangles, each with base equal to the length of the longer sides of the larger rectangle and with perpendicular height equal to half the length of the shorter sides of the larger rectangle. Therefore the area of each triangle is equal to half the area of the smaller rectangle. Since each triangle is half of the three shaded squares, the area of each triangle, in cm2 , is (3 × 25) ÷ 2 = 37.5. Hence the area of the larger rectangle, in cm2 , is 4 × 37.5 = 150.
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