Question

[answer asap]

the perimeter of the original rectangle on the left is 30 meters. the perimeter of the reduced rectangle on the right is 24 meters.

[see image]

what is x, the width of the original rectangle on the left? round to the nearest hundredth if necessary.

Answer 1

Answer:

The width of the original rectangle on the left is $5\ m$

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

so

Let

z -----> the scale factor

a ----> perimeter of the reduced rectangle on the right

b ----> perimeter of the original rectangle on the left

$z=\frac{a}{b}$

we have

$a=24\ m$

$b=30\ m$

substitute

$z=\frac{24}{30}=0.8$

step 2

Find the width of the reduced rectangle on the right

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$

we have

$L=8\ m$

$P=24\ m$

substitute and solve for W

$24=2(8+W)$

$12=(8+W)$

$W=12-8=4\ m$

step 3

Find the width of the original rectangle on the left

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

so

Let

z -----> the scale factor

y ----> the width of the reduced rectangle on the right

x ----> the width of the original rectangle on the left

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

we have

$y=4\ m$

$z=0.8$

substitute and solve for x

$0.8=\frac{4}{x}$

$x=\frac{4}{0.8}$

$x=5\ m$