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# The diagonal length of a square is 14.1 sq. units. What is the area of

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The diagonal length of a square is 14.1 sq. units. What is the area of  [#permalink]

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19 Aug 2010, 21:16
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Difficulty:

95% (hard)

Question Stats:

23% (02:24) correct 77% (01:09) wrong based on 59 sessions

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The diagonal length of a square is 14.1 sq. units. What is the area of the square, rounded to the nearest integer? ($$\sqrt{2}$$ is approximately 1.41)

(A) 96
(B) 97
(C) 98
(D) 99
(E) 100

Source: Nova's Math Bible
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Joined: 10 Jul 2010
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Re: The diagonal length of a square is 14.1 sq. units. What is the area of  [#permalink]

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19 Aug 2010, 22:07

Diagonal cuts the square into two equal triangles.

Ratio of the sides are 1 : 1 :root(2)

root(2)=14.1

So each side = 10.

Area =10x10 =100

What is the source of the question?
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Re: The diagonal length of a square is 14.1 sq. units. What is the area of  [#permalink]

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19 Aug 2010, 22:17
If a is the length of a side of the square, then a diagonal divides the square into two congruent (equal) right
triangles. Applying The Pythagorean Theorem to either triangle yields diagonal^2 = side^2 + side2^ = a^2 + a^2 =
2a^2. Taking the square root of both sides of this equation yields diagonal = a 2 . We are given that the
diagonal length is 14.1. Hence, a*sqrt(2) = 14.1 or a = 14.1/sqrt(2)

Now, the area, a^2, equals [14.1/sqrt(2)]^2 ==> 14.1^2 / 2

==> 198.81/2 => 99.4

The number 99.4 is nearest to 99. Hence, the answer is (D).

Note: If you had approximated 14.1/sqrt(2) with 10, you would have mistakenly gotten 100 and would have
answered (E). Approximation is the culprit. Prefer doing it in the last.

This problem was from Nova's Math Bible
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Re: The diagonal length of a square is 14.1 sq. units. What is the area of  [#permalink]

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19 Aug 2010, 22:19
2
Hi,

If we look at 14.1 as root(2) times 10; then the answer is E.

But, if we treat it as just 14.1, then the answer is D.

I doubt if GMAT would test students at this approximation level - after (kind of) misleading in the question that root(2) is approximately 1.41.
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Re: The diagonal length of a square is 14.1 sq. units. What is the area of  [#permalink]

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20 Aug 2010, 02:36
Ya, I agree...I also got E...but nice explanation given by @Qweert
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Re: The diagonal length of a square is 14.1 sq. units. What is the area of  [#permalink]

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20 Aug 2010, 05:29
qweert wrote:
Q. The diagonal length of a square is 14.1 sq. units. What is the area of the square, rounded to the nearest
integer? (sqrt 2 is approximately 1.41.)

(A) 96
(B) 97
(C) 98
(D) 99
(E) 100

Can someone explain why the answer is not E?

There is a shortcut for this problem. Rather than calculating the sides of a square we can recall that the area of a square (as the area of a rhombus) equals to half of the product of diagonals --> $$area=\frac{d^2}{2}=\frac{14.1^2}{2}=99.4$$ --> area rounded to the nearest integer equals to 99.

P.S. I don't think GMAT will ever mislead you like this.
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Re: The diagonal length of a square is 14.1 sq. units. What is the area of  [#permalink]

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21 Aug 2010, 08:11
This was from Nova Math Bible..

Even i though it was misleading rather than tricky!
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Re: The diagonal length of a square is 14.1 sq. units. What is the area of  [#permalink]

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08 Jul 2017, 05:22
there is a mistake in this question. How can length of a diagonal have square units? length has only one dimension.
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Re: The diagonal length of a square is 14.1 sq. units. What is the area of  [#permalink]

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08 Jul 2017, 06:00
[quote="Bunuel"][quote="qweert"]Q. The diagonal length of a square is 14.1 sq. units. What is the area of the square, rounded to the nearest
integer? (sqrt 2 is approximately 1.41.)

(A) 96
(B) 97
(C) 98
(D) 99
(E) 100

what if we look at this question in this way?

14.1 = a * root(3) [diagnol of square]

a= 14.1 / root(3)

area of square = a * a

area = (14.1 * 14.1 ) / 3

i dont knw what im doing wrong
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Re: The diagonal length of a square is 14.1 sq. units. What is the area of  [#permalink]

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11 Jul 2017, 01:01
4gmatmumbai wrote:
Hi,

If we look at 14.1 as root(2) times 10; then the answer is E.

But, if we treat it as just 14.1, then the answer is D.

I doubt if GMAT would test students at this approximation level - after (kind of) misleading in the question that root(2) is approximately 1.41.

I agree, I don't think that they would mention the approximate value of root(2), if it was not to be used in the question. Particularly, when it literally chops off the step of division.
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Re: The diagonal length of a square is 14.1 sq. units. What is the area of   [#permalink] 11 Jul 2017, 01:01
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