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19 Aug 2010, 21:16
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
23% (01:57) correct
77%
(01:12)
wrong
based on 56
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
(A) 96
(B) 97
(C) 98
(D) 99
(E) 100
Source: Nova's Math Bible
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19 Aug 2010, 22:07
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Answer should be E.
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?
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?
19 Aug 2010, 22:17
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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
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
