Question

The widths of two similar rectangles have a ratio of 2:6 . The area of the smaller rectangle is 12 ft2. What is the area of the larger rectangle? Enter your answer in the box.

Answer 1

The area of the larger rectangle is
`108\ ft^(2)`

Explanation:

we know that

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

and the ratio of its corresponding sides is equal to the scale factor

Let

z-----> the scale factor

x-----> the area of small rectangle

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

so

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

we have

`z=2/6`

`x=12\ ft^(2)`

substitute and solve for y

`(2/6)^(2) =(12)/(y)`

`y=12/(4/36)=108\ ft^(2)`