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The sides of a rectangular region measured to the nearest

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gmihir
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The sides of a rectangular region measured to the nearest [#permalink] New post   19 May 2012, 08:53
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The sides of a rectangular region measured to the nearest centimeter are 8 cm and 6 cm. Out of the following which is the largest possible value of actual area of rectangle ?

A. 48
B. 55.25
C. 52.29
D. 44
E. 41.25

I tried considering larget posible sides as 8.44cm and 6.44cm but couldn't get the answer. What would be the correct measure of largest possible sides of rectangle in this case ?
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Re: The sides of a rectangular region measured to the nearest [#permalink] New post   20 May 2012, 12:30
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gmihir wrote:
The sides of a rectangular region measured to the nearest centimeter are 8 cm and 6 cm. Out of the following which is the largest possible value of actual area of rectangle ?

A. 48
B. 55.25
C. 52.29
D. 44
E. 41.25

I tried considering larget posible sides as 8.44cm and 6.44cm but couldn't get the answer. What would be the correct measure of largest possible sides of rectangle in this case ?


Given: \(7.5<a<8.5\) and \(5.5<b<6.5\), where a and b are the sides of the rectangle.

So, the largest area the rectangle can possibly have is a bit less than \(8.5*6.5=55.25\). The correct answer would be the largest value among the options which is less than 55.25, so 52.29. For example the sides can be: 8.3 and 6.3 --> 8.3*6.3=52.29.

Answer: C.

Hope it's clear.
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seabhi
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Re: The sides of a rectangular region measured to the nearest [#permalink] New post   29 Dec 2013, 23:51
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"a" can be anywhere between 7.5 and 8.4 and "b" can be anywhere between 5.5 and 6.4.
Hence max area can be 8.4*6.4 eq 53.76.
largest value which is near to 53.76 is 52.29.

Hence C.
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Re: The sides of a rectangular region measured to the nearest [#permalink] New post   01 Jan 2016, 19:19
got to the right answer in 1 minute.

since we have rounded to the nearest cm, and we are asked for the maximum possible area, then we have to maximize the values of length and width.
7.5<L<8.5
5.5<W<6.5

suppose L = 8.4 and W=6.4

8.4*6.4=53.76. since we need to have a value around this number, only C fits in.

I tried 8.49 and 6.49. the value is 55.1001. since we put more 9's after the decimal points, the number will increase, but very very little. thus, it can't be B.
48 cannot be the maximum value, and everything below 48 as well.
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Re: The sides of a rectangular region measured to the nearest [#permalink] New post   27 Jun 2023, 13:41
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gmihir wrote:
The sides of a rectangular region measured to the nearest centimeter are 8 cm and 6 cm. Out of the following which is the largest possible value of actual area of rectangle ?

A. 48
B. 55.25
C. 52.29
D. 44
E. 41.25


If l’=8 and w’=6 are the rounded-to-integer values of the length and width of the rectangle, then according to the conventional rounding rule, the following must be true about the actual values:

7.5 ≤ l < 8.5

5.5 ≤ w < 6.5

Since all sides are positive in the inequalities above, we can multiply the corresponding sides to have:

(7.5)(5.5) ≤ lw < (8.5)(6.5)

41.25 ≤ lw < 55.25

We see that among the given choices, 52.29 is the largest possible value of the actual area.

Answer: C

(Note: The question stem should ask for the largest possible value of the actual area in square centimeters.)
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Re: The sides of a rectangular region measured to the nearest [#permalink]
27 Jun 2023, 13:41
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