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Nesterboy [21]
2 years ago
5

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. A small rectangle has a length of 9 meters. A larger rectangle is blank. Not drawn to scale What is the width of the original rectangle? 20 meters 24 meters 36 meters 48 meters
Mathematics
2 answers:
Reika [66]2 years ago
7 0

Answer:

b 24 meters

Step-by-step explanation:

ed

Whitepunk [10]2 years ago
6 0

Answer:

<u>24 meters</u> is the width of the original rectangle.

Step-by-step explanation:

Given:

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 rectangle has a length of 9 meters.

Now, to get the width of original rectangle.

The reduced rectangle's perimeter = 30 meters.

The reduced rectangle's length = 9 meters.

Now, we find the width of reduced rectangle by using formula:

Let the width of reduced rectangle be x.

Perimeter=2\times length+2\times width

30=2\times 9+2\times x

30=18+2x

<em>Subtracting both sides by 18 we get:</em>

<em />12=2x<em />

<em>Dividing both sides by 2 we get:</em>

6=x\\\\x=6\ meters.

The width of reduced rectangle = 6 meters.

Now, to get the width of original rectangle:

Let the width of original rectangle be w.

<em>As given, the perimeter of the original rectangle = 120 meters.</em>

<em>And, the perimeter of reduced rectangle is 30 meters and its width is 6 meters.</em>

<em>So, 30 is equivalent to 6.</em>

<em>Thus, 120 is equivalent to </em>w.<em />

Now, to get the width using cross multiplication method:

\frac{30}{6}=\frac{120}{w}

<em>By cross multiplying we get:</em>

<em />30w=720<em />

<em>Dividing both sides by 30 we get:</em>

<em />w=24\ meters.<em />

<em>The width of original rectangle = 24 meters.</em>

Therefore, 24 meters is the width of the original rectangle.

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