Question

Pls help fast I have to submit this soon!! :)

Answer 1

Since the rectangles are similar, that means their sides are proportional.

Since the bigger rectangle has a base of 24cm and the smaller one's base is 20cm, the proportion the sides hold is

`(24)/(20)=1.2`

This means the sides of the larger rectangle are 1.2 times larger than those of the smaller one.

The area of the small rectangle is 80cm². Since

`A=b\mathrm{}h`

where b is the lenght of the base and h is the lenght of the height, then

`80=20\cdot h_1`
`(80)/(20)=h_1=4`

So the height of the small rectangle will be 4cm. But as we previously deduced, the height of the larger rectangle will be 1.2 times larger than that of the smaller one, so it's height will be

`h_2=4\cdot1.2=4.8`

And so, its are is

`A_2=24\cdot4.8=115.2`

We can confirm this because

`(115.2)/(80)=1.44=1.2^2`

which is the proportion the areas of the rectangles hold.