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The diagonal length of a square is 14.1 sq. units. What is t
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17 Mar 2019, 02:49
17 Mar 2019, 02:49
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Question Stats:
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50% (00:51) wrong based on 6 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?
(A) 96
(B) 97
(C) 98
(D) 99
(E) 100
(A) 96
(B) 97
(C) 98
(D) 99
(E) 100
Re: The diagonal length of a square is 14.1 sq. units. What is t
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20 Mar 2019, 11:05
20 Mar 2019, 11:05
Expert Reply
The diagonal of the square will be the hypotenuse of an isosceles right triangle, two sides of which are sides of the square.
So, if I call each side of the square x, then using the Pythagorean theorem:
\(x^{2} + x^{2} = (14.1)^{2}\)
\(2x^{2} = (14.1)^{2}\)
Taking the square root of both sides:
\(\sqrt{2}x = 14.1\)
Divide by the square root of 2:
\(x = \frac{14.1}{\sqrt{2}}\)
Now that we have x, one side of the square, we can find the area, x²:
\(x^{2} = \frac{(14.1)^{2}}{2}\)
Using a calculator, (14.1)² = 198.81. Divided by 2 we get 99.405. That rounds down to the nearest integer, 99.
Alternatively, we might know that an isosceles right triangle is a 45-45-90 triangle whose sides have the ratio \(x:x:\sqrt{2}x\). Since the hypotenuse is 14.1, then \(\sqrt{2}x = 14.1\). Divide both sides by \(\sqrt{2}\) and we get \(x = \frac{14.1}{\sqrt{2}}\). Then we can proceed as above.
So, if I call each side of the square x, then using the Pythagorean theorem:
\(x^{2} + x^{2} = (14.1)^{2}\)
\(2x^{2} = (14.1)^{2}\)
Taking the square root of both sides:
\(\sqrt{2}x = 14.1\)
Divide by the square root of 2:
\(x = \frac{14.1}{\sqrt{2}}\)
Now that we have x, one side of the square, we can find the area, x²:
\(x^{2} = \frac{(14.1)^{2}}{2}\)
Using a calculator, (14.1)² = 198.81. Divided by 2 we get 99.405. That rounds down to the nearest integer, 99.
Alternatively, we might know that an isosceles right triangle is a 45-45-90 triangle whose sides have the ratio \(x:x:\sqrt{2}x\). Since the hypotenuse is 14.1, then \(\sqrt{2}x = 14.1\). Divide both sides by \(\sqrt{2}\) and we get \(x = \frac{14.1}{\sqrt{2}}\). Then we can proceed as above.
gmatclubot
Re: The diagonal length of a square is 14.1 sq. units. What is t [#permalink]
20 Mar 2019, 11:05
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