Question

Two rectangles are similar. The smaller has a length of 8 cm and an area of 40 cm.

If the width of the larger rectangle is 10 cm, find its area.

Answer 1

160 cm²

Explanation:

If the two rectangles are similar, that means they have equal scale factors. The smaller rectangle has length of 8 cm and area of 40 cm, which means the width is 5 cm.

The width of the larger rectangle is 10 cm, which is double the width of the smaller, similar rectangle. So, to find the length of the larger rectangle, multiply 8 x 2, which gives you 16 cm for the length, since the scale factor is 2.

Now, just find the area of the larger rectangle by doing length x width. 16cm x 10 cm = 160 cm²

Answer 2

160 cm^2

Explanation:

Our strategy is to find the length of the larger rectangle so we can find the area. To find the length, we will rely on the fact the two rectangles are "similar": their sides are in equal proportions, or have the same "ratio."

We know that the smaller rectangle has a width of 5 cm because, when we substitute area and length into

A = lw

we get

40 = 8w

w = 5

when we divide both sides by 8.

Because of equal proportions:

Width : length of the smaller rectangle = Width : length of the larger rectangle

We can write an equation

5 / 8 = 10 / x

Cross multiply

5x = 80

x = 16

So the larger rectangle has a length of 16 cm and a width of 10 cm (given)

meaning the area is

16 * 10 = 160 cm^2