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3 years ago

14

Bobby knows that the perimeter of the original rectangle is 120 meters. He also knows that the perimeter of the reduced rectangl

e is 30 meters and the reduced length is 9 meters.

2 answers:

olga nikolaevna [1]3 years ago

5 0

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

Maurinko [17]3 years ago

3 0

The question is

What are the dimensions of the original rectangle?

Step 1

<u>Find the scale factor</u>

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

<u>Find the width of the reduced rectangle</u>

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

<u>Find the dimensions of the original rectangle</u>

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 $36\ m\ *\ 24\ m$

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Step-by-step explanation:

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Step-by-step explanation:

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The diagrammatic expression below clearly interprets the question.

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