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

Answer:

The ratio of the areas of the smaller rectangle to the larger rectangle is  $\frac{1}{9}$

Step-by-step 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

$z^{2}=\frac{x}{y}$

substitute the values

$z^{2}=\frac{20}{180}$

simplify

$z^{2}=\frac{1}{9}$

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

$z=\frac{1}{3}$ ------> the scale factor

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