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A painting 4.5 ft X 1.4 ft is to be bordered with a 3 inches wide wood

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A painting 4.5 ft X 1.4 ft is to be bordered with a 3 inches wide wood  [#permalink]

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New post 04 Mar 2019, 07:30
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A
B
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  95% (hard)

Question Stats:

8% (05:31) correct 92% (02:22) wrong based on 12 sessions

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A painting 4.5 ft X 1.4 ft is to be bordered with a 3 inches wide wooden strip. What is the minimum length of the strip required to border the painting?

A. 13
B. 14
C. 15
D. 16
E. 17
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Re: A painting 4.5 ft X 1.4 ft is to be bordered with a 3 inches wide wood  [#permalink]

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New post 06 Mar 2019, 03:36
Top Contributor
Hello,

Greetings for the day.

Although this question looks like a simple question on mensuration, there is a trick element involved in it, and therefore, it is very easy to make calculation mistakes.

We are required to find the length of the strip required to border the painting.
The dimensions of the painting are 4.5 feet by 1.4 feet. This is a rectangle.
If we draw a border of 3 inches width, we will obtain a rectangle which is both longer and wider, around the painting. Because we have to calculate the length of this border, essentially, we are required to calculate the perimeter of the outer rectangle.

Also, since the width of the border is given in inches, whereas the dimensions of the painting are given in feet, it’s a good idea to convert feet to inches.

1 foot = 12 inches.

Therefore, 4.5 feet = 4 feet + 0.5 feet = 48 + 6 = 54 inches
and 1.4 feet = 1 feet + 0.4 feet = 12 + 4.8 = 16.8 inches

The whole situation above can be represented as shown in the diagram below.

Attachment:
GMAT Club - 05032019.jpg
GMAT Club - 05032019.jpg [ 33.53 KiB | Viewed 119 times ]



We can see from the figure that the length of the outer rectangle is 60 inches and the width of the outer rectangle is 22.8 inches.
Hence, the minimum length of the border has to be 60 inches and the minimum width has to be 22.8 inches.
Now, 60 inches = 5 feet and 1feet< 22.8 inches < 2 feet.
Since all the options are given in terms of integers, the minimum width of the border has to be 24 inches I.e. 2 feet. Therefore, the minimum perimeter of the outer rectangle will have to be 2(60 + 24) = 168 inches which is nothing but 14 feet.

There we go, the correct answer option is B.

A point to be noted here is the importance of being good at conversions. If you are well versed with the basic conversions, then you will be in a great position to convert this question from a tricky question to an easy question.

Hope this helps!
Cheers.
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Re: A painting 4.5 ft X 1.4 ft is to be bordered with a 3 inches wide wood   [#permalink] 06 Mar 2019, 03:36
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