Question

A rectangle that is 8 centimeters long has an area of 100 square centimeters. A similar rectangle has an area of 16 square centimeters. What is the width of the smaller rectangle

Answer 1

The width of the smaller rectangle is 5 centimeters

Explanation:

step 1

Find the scale factor

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

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

we have

`x=16\ cm^2\\y=100\ cm^2`

substitute

`z^(2)=(16)/(100)`

square root both sides

`z=(4)/(10)`

step 2

Find the width of the larger rectangle

we know that the area is equal to

`A=LW`

we have

`A=100\ cm^2\\L=8\ cm`

substitute

`100=8W\\W=12.5\ cm`

step 3

Find the width of the smaller rectangle

To find out the width of the smaller rectangle, multiply the width of the larger rectangle by the scale factor

so

`12.5((4)/(10))=5\ cm`