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What is the approximate minimum length of a rope required to enclose an area of 154 square meters?

A. 154 B. 60 C. 57 D. 50 E. 44

Since a circle has the minimum possible perimeter for a given area, then in order to minimize the length of a rope it should enclose a circle.

So, 154 square meters should be the area of a circle: \(area=\pi r^2=154\). Now, the approximate value of \(\pi\) is \(\frac{22}{7}\), hence \(\frac{22}{7}*r^2=154\), which gives \(r^2 \approx 49\) and finally \(r \approx 7\).

The length of a rope will equal to the circumference of the circle: \(circumference=2\pi r \approx 2*\frac{22}{7}*7=44\).

What is the approximate minimum length of a rope required to enclose an area of 154 square meters?

A. 154 B. 60 C. 57 D. 50 E. 44

Since a circle has the minimum possible perimeter for a given area, then in order to minimize the length of a rope it should enclose a circle.

So, 154 square meters should be the area of a circle: \(area=\pi r^2=154\). Now, the approximate value of \(\pi\) is \(\frac{22}{7}\), hence \(\frac{22}{7}*r^2=154\), which gives \(r^2 \approx 49\) and finally \(r \approx 7\).

The length of a rope will equal to the circumference of the circle: \(circumference=2\pi r \approx 2*\frac{22}{7}*7=44\).

Answer: E

Ohk..!Thanks Bunuel..!Could you please tell which shape be chosen when we are given the area and maximum length of the rope is to be found out ? Thanks again..!
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ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD.

What is the approximate minimum length of a rope required to enclose an area of 154 square meters?

A. 154 B. 60 C. 57 D. 50 E. 44

Since a circle has the minimum possible perimeter for a given area, then in order to minimize the length of a rope it should enclose a circle.

So, 154 square meters should be the area of a circle: \(area=\pi r^2=154\). Now, the approximate value of \(\pi\) is \(\frac{22}{7}\), hence \(\frac{22}{7}*r^2=154\), which gives \(r^2 \approx 49\) and finally \(r \approx 7\).

The length of a rope will equal to the circumference of the circle: \(circumference=2\pi r \approx 2*\frac{22}{7}*7=44\).

Answer: E

Ohk..!Thanks Bunuel..!Could you please tell which shape be chosen when we are given the area and maximum length of the rope is to be found out ? Thanks again..!

You don';t need this for the GMAT, but anyway, for a given area, the perimeter is NOT limited.

For example, consider a rectangle with the area of 100. If the width approaches 0, then the length approaches infinity, which means that the perimeter is also approaches infinity.
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I just wanted to clarify is it square or circle which has the minimum perimeter for the given area As per one of the GMAT guides = "Of all quadrilaterals with a given area, the square has the minimum perimeter."

I guess the question should have mentioned a "circular" area. Because nothing is telling us that we are supposed to find a circumference instead of a perimeter. I went with a rectangular of 11 14 too.
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I just wanted to clarify is it square or circle which has the minimum perimeter for the given area As per one of the GMAT guides = "Of all quadrilaterals with a given area, the square has the minimum perimeter."

Thanks

I don't think you can compare a circle to a quadri since you don't use the same input to compute them. Your statement is true but only applies to quadris. The trick here was that we weren't given the shape de la landbank and that the quadri was easy to spot.
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I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Why pai is 22/7?

The question asks about the approximate length.

\(\pi = 3.1415...\) and 22/7 = 3.142..., and since we need only approximate value we can use 22/7 instead of \(\pi\) to simplify calculations.
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I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Hello,

Sorry, I am not clear as to how to determine this question is referring to the area of a 'circle'? I am not clear with what question is in fact asking.