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Sub 505 (Easy)|   Geometry|            
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Bunuel
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If the area of a square region having sides of length 6 centimeters is 01 Aug 2018, 23:26
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E
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97% (00:57) correct 3% (01:23) wrong based on 579 sessions

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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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E
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If the area of a square region having sides of length 6 centimeters is 01 Aug 2018, 23:33
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Bunuel
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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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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If the area of a square region having sides of length 6 centimeters is 06 Aug 2021, 06:56
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Bunuel
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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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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If the area of a square region having sides of length 6 centimeters is 03 Jun 2023, 06:12
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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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