Michel uses the scale drawing and the scale factor to enlarge a square that has a side length of 12 in. A square with side lengt
hs of 12 inches. Scale factor: 3 inches = 2 meters. Which proportion could Michel use to solve the side length, x, of the enlarged square? StartFraction 3 inches over 2 meters EndFraction = StartFraction x meters over 12 inches EndFraction StartFraction x inches over 2 meters EndFraction = StartFraction 3 inches over 12 meters EndFraction StartFraction 3 inches over x meters EndFraction = StartFraction 2 meters over 12 inches EndFraction StartFraction 3 inches over 2 meters EndFraction = StartFraction 12 inches over x meters EndFraction
The scale factor used by Michel in the given scenario is 3 inches = 2 meters. It means that 3 inches on the drawing represents 2 metres on the actual or enlarged square. If the length of the enlarged square is x, the calculation for x would be as follows:
3/2 = 12/x
Cross multiplying, it becomes
3x = 2 × 12 = 24
x = 24/3
x = 8 meters
Therefore, the proportion that Michel could use to solve the side length, x, of the enlarged square is
StartFraction 3 inches over 2 meters EndFraction = StartFraction 12 inches over x meters EndFraction
The similar shortcut for division works because division is the opposite operation of multiplication—it “undoes” multiplication. If we move the decimal point to the right when multiplying by 10, 100, 1000 and so on, then it is quite natural that the rule for division would work the “opposite” way.
