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# The sides of a rectangular region measured to the nearest

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Intern
Joined: 04 Mar 2012
Posts: 37
The sides of a rectangular region measured to the nearest  [#permalink]

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19 May 2012, 08:53
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Difficulty:

65% (hard)

Question Stats:

50% (01:30) correct 50% (01:33) wrong based on 109 sessions

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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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Joined: 02 Sep 2009
Posts: 58445
Re: The sides of a rectangular region measured to the nearest  [#permalink]

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20 May 2012, 12:30
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1
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.

Hope it's clear.
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Re: The sides of a rectangular region measured to the nearest  [#permalink]

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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]

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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]

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27 Mar 2019, 08:20
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Re: The sides of a rectangular region measured to the nearest   [#permalink] 27 Mar 2019, 08:20
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