Question

A rectangle has an area of 20 square feet a similar rectangle has an area of 180 square feet what is ratio of the areas of these similar rectangles

Answer 1

The ratio of the areas of the smaller rectangle to the larger rectangle is
`(1)/(9)`

Explanation:

we know that

if two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> the area of the smaller rectangle

y----> the area of the larger rectangle

so

`z^(2)=(x)/(y)`

substitute the values

`z^(2)=(20)/(180)`

simplify

`z^(2)=(1)/(9)`

That means, the area of the larger rectangle is 9 times the area of the smaller rectangle

`z=(1)/(3)` ------> the scale factor

That means, the dimensions of the larger rectangle is 3 times the dimensions of the smaller rectangle