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. A small rectangle has a length of 9 meters. A larger rectangle is blank. What is the width of the original rectangle?

Question

Mathematics

Karly Barajas

31 October, 23:23

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. A small rectangle has a length of 9 meters. A larger rectangle is blank. What is the width of the original rectangle?

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Answers (1)

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Michael Chambers · Answer 1

the width in the original rectangle is 24 meters.

Step-by-step explanation:

We know the perimeters of both rectangles therefore we can calculate the scale in this way:

120/30 = 4

Which means that there is a 4: 1 scale between the original and the reduced rectangle.

We know that the length in the reduced rectangle is 9, therefore in the original it would be:

9 * 4 = 36

Which means that 36 meters is the length of the original rectangle. We know that the perimeter is equal to:

p = 2 * l + 2 * w

replacing:

120 = 2 * 36 + 2 * w

2 * w = 120 - 72

w = 48/2

w = 24

Which means that the width in the original rectangle is 24 meters.