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butalik [34]
3 years ago
6

a rectangle measures by 3 cm by 4 cm. a rectangle similar to the first measures 12 cm by 16 cm. find the ratio of the areas of r

ectangles. how does that ratio compare with the ratio of the side lengths?
Mathematics
1 answer:
kumpel [21]3 years ago
6 0
The side that measures 12 cm corresponds to the side that measures 3 cm.
The side that measures 16 cm corresponds to the side that measures 4 cm.
The ratio of the side lengths is (12 cm)/(3 cm) = (16 cm)/(4 cm) = 4

Now let's calculate the two areas.

For the 3 cm by 4 cm rectangle:
A = LW = 3 cm * 4 cm = 12 cm^2

For the 12 cm by 16 cm rectangle:
A = LW = 12 cm * 16 cm = 192 cm^2

The ratio of the areas is (192 cm^2)/(12 cm^2) = 16

The ratio of the areas is 16.
The ratio of side lengths is 4.
Notice that 16 = 4^2.
The ratio of the areas is the square of the ratio of the side lengths.
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