Question

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.

Answer 1

The width of the reduced rectangle is. 6 then multiplely by 4 to get to the original
So the length of the original is36 and the width is 24 meters

Answer 2

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

$scale\ factor=\frac{Perimeter\ original \ rectangle}{Perimeter\ reduced\ rectangle}$

we have

$Perimeter\ original \ rectangle=120\ m$

$Perimeter\ reduced \ rectangle=30\ m$

Substitute the values

$scale\ factor=\frac{120}{30}=4$

therefore

the scale factor is $4$

Step 2

Find the width of the reduced rectangle

we know that

The perimeter of a rectangle is equal to

$P=2L+2W$

where

L is the length side of the rectangle

W is the width side of the rectangle

Reduced rectangle

we have

$L=9\ m$

$P=30\ m$

substitute

$30=2*9+2W$

$30=18+2W$

Solve for W

$2W=30-18$

$W=12/2=6\ m$

therefore

The dimensions of the reduced rectangle are $9\ m\ *\ 6\ m$

Step 3

Find the dimensions of the original rectangle

Original Length

we know that

$original\ length=scale\ factor*reduced\ length$

we have

$reduced\ length=9\ m$

$scale\ factor=4$

substitute

$original\ length=4*9=36\ m$

Original Width

we know that

$original\ width=scale\ factor*reduced\ width$

we have

$reduced\ width=6\ m$

$scale\ factor=4$

substitute

$original\ width=4*6=24\ m$

therefore

The dimensions of the original rectangle are $36\ m\ *\ 24\ m$