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# Geometry

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A rectangle is divided into smaller rectangles as shown.   Several of the small rectangles are labelled with their area.  Find x.

May 13, 2022

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Let w be the length of the top side of the top-left rectangle. Then the left side of the top-left rectangle is $$\dfrac 3w$$ and the left side of the bottom-left rectangle is $$\dfrac 7w$$. This suggests the heights of the rectangle are in the ratio 3 : 7.

Since the top side of the top-right rectangle and that of the bottom-right rectangle are the same, the area ratio of the top-right rectangle and that of the bottom-right rectangle is also 3 : 7, which means $$x = 12 \times \dfrac 73 = 28$$.

May 14, 2022