Bobby knows that the perimeter of the original rectangle is 120 meters. he also knows that the perimeter of the reduced rectangle is 30 meters and the reduced length is 9 meters.

The length of the original rectangle is 36 meters and the width is 24 meters.

A scaled diagram is a reduced form in terms of dimensions of an original image / building / object.

Scale of the drawing = original dimensions / dimensions of the scale drawing

= 120 / 30

= 4

Length = 9 x 4 = 36 meters

Width = (perimeter / 2) - length

= (120 / 2) - 36

= 60 - 36

= 24 meters

To learn more about a rectangle, please check: link

The question is

What are the dimensions of the original rectangle?

Step 1

Find the scale factor

we know that

The scale factor is equal to

we have

Substitute the values

therefore

the scale factor is

Step 2

Find the width of the reduced rectangle

we know that

The perimeter of a rectangle is equal to

where

L is the length side of the rectangle

W is the width side of the rectangle

Reduced rectangle

we have

substitute

Solve for W

therefore

The dimensions of the reduced rectangle are

Step 3

Find the dimensions of the original rectangle

Original Length

we know that

we have

substitute

Original Width

we know that

we have

substitute

therefore

The dimensions of the original rectangle are

a negative exponent is translated as follows:

so, we have

entering that problem on the tube might get you an answer