Question

Two picture frames are similar. The ratio of the perimeters of the two pieces is 3:5. If the area of the smaller frame is 108 square inches, what
is the area of the larger frame?

Answer 1

Answer:

The area of the larger frame is 300 square inches

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

In this problem the ratio of the perimeters is 3:5

so

The scale factor is 3/5

step 2

Find the area of the larger frame

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 frame

y ----> the area of the larger frame

so

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

we have

$z=\frac{3}{5}$

$x=108\ in^2$

substitute

$(\frac{3}{5})^{2}=\frac{108}{y}$

$\frac{9}{25}=\frac{108}{y}$

solve for y

$y=\frac{108}{9}(25)$

$y=300\ in^2$

therefore

The area of the larger frame is 300 square inches