A rectangle is divided into smaller rectangles as shown. Several of the small rectangles are labelled with their area. Find x.
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 \(x = 12 \times \dfrac 73 = 28\).