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If the area of a square region having sides of length 6 centimeters is

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Bunuel
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If the area of a square region having sides of length 6 centimeters is [#permalink] New post   01 Aug 2018, 23:26
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If the area of a square region having sides of length 6 centimeters is equal to the area of a rectangular region having width 2.5 centimeters, then the length of the rectangle, in centimeters, is

A. 8.5
B. 9.5
C. 9.6
D. 10.5
E. 14.4
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If the area of a square region having sides of length 6 centimeters is [#permalink] New post   01 Aug 2018, 23:33
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Bunuel wrote:
If the area of a square region having sides of length 6 centimeters is equal to the area of a rectangular region having width 2.5 centimeters, then the length of the rectangle, in centimeters, is

A. 8.5
B. 9.5
C. 9.6
D. 10.5
E. 14.4


From the question stem, we can deduce that the areas must be the same.

Since we can equate the area of a rectangle to that of a square,
\(side^2 = length * breadth\) -> \(length = \frac{side^2}{breadth}\)

Therefore, the length of the rectangle is \(\frac{6^2}{\frac{5}{2}} = \frac{36*2}{5} =\) 14.4(Option E)
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Re: If the area of a square region having sides of length 6 centimeters is [#permalink] New post   06 Aug 2021, 06:56
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Bunuel wrote:
If the area of a square region having sides of length 6 centimeters is equal to the area of a rectangular region having width 2.5 centimeters, then the length of the rectangle, in centimeters, is

A. 8.5
B. 9.5
C. 9.6
D. 10.5
E. 14.4


Given: (area of square) = (area of rectangle)
In other words: (width)(length) = (width)(length)
Plug-in information: (6)(6) = (2.5)(x)
Evaluate: 36 = 2.5x
Solve: x = 36/2.5 = 14.4

Answer: E
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Re: If the area of a square region having sides of length 6 centimeters is [#permalink] New post   03 Jun 2023, 06:12
The area of a square is given by the formula A = s^2, where A is the area and s is the length of a side.

In this case, the area of the square region with side length 6 centimeters is 6^2 = 36 square centimeters.

The area of a rectangle is given by the formula A = l * w, where A is the area, l is the length, and w is the width.

We are given that the area of the rectangular region is equal to the area of the square, so we have:

36 square centimeters = l * 2.5 centimeters

To find the length of the rectangle, we can divide both sides of the equation by 2.5 centimeters:

l = 36 square centimeters / 2.5 centimeters≈ 14.4 centimeters

Therefore, the length of the rectangle is approximately 14.4 centimeters, which corresponds to option (E).
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Re: If the area of a square region having sides of length 6 centimeters is [#permalink]
03 Jun 2023, 06:12
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