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If a square mirror has a 30-inch diagonal, what is the area of the mir

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Bunuel
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If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink] New post   17 Feb 2016, 03:32
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If a square mirror has a 30-inch diagonal, what is the area of the mirror, in inches?

A. 225
B. 450
C. 600
D. 750
E. 900


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B
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TeamGMATIFY
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If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink] New post   23 Feb 2016, 04:08
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Bunuel wrote:
If a square mirror has a 30-inch diagonal, what is the area of the mirror, in inches?

A. 225
B. 450
C. 600
D. 750
E. 900


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Diagonal of a mirror = \(\sqrt{2}\)*side
Therefore
\(\sqrt{2}\)*side = 30
Side = 30/\(\sqrt{2}\)

Area = 30/\(\sqrt{2}\) * 30/\(\sqrt{2}\) = 900/2 = 450
Option B
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Re: If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink] New post   17 Feb 2016, 04:10
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Bunuel wrote:
If a square mirror has a 30-inch diagonal, what is the area of the mirror, in inches?

A. 225
B. 450
C. 600
D. 750
E. 900


Kudos for correct solution.


Let's name square sides of s, using pythagoras 30^2=s^2+s^2, this ends to s=\sqrt{450}, which is \sqrt{2*3^2*5^2}, hence square sides are 15\sqrt{2}, 15\sqrt{2}*15\sqrt{2}=450, hence, i think the correct answer is B.
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Re: If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink] New post   09 Apr 2016, 14:35
(30/sqrt 2)^2 = 450
Correct answer - B
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Re: If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink] New post   10 Jun 2016, 14:15
Bunuel wrote:
AbdurRakib wrote:
If a square mirror has a 30-inch diagonal, what is the area of the mirror, in inches?

A. 225

B. 450

C. 600

D. 750

E. 900


Merging topics. Please search before posting.


Thanks But,
Actuality I searched on the Google but found only this link if-a-square-mirror-has-a-20-inch-diagonal-what-is-the-99359.html

I'll search it next time on GMATCLUB to avoid mistake

Thanks again
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If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink] New post   14 Jun 2016, 00:18
Bunuel wrote:
If a square mirror has a 30-inch diagonal, what is the area of the mirror, in inches?

A. 225
B. 450
C. 600
D. 750
E. 900


Kudos for correct solution.


If a square has a side a, then the length of the diagonal is \(a* \sqrt{2}\)

Area of square would be \(a^2\)

\(a\sqrt{2}\) = 30;

squaring both sides
2\(a^2\) = 30*30 = 900
\(a^2\) = 450 --> This is the area.

Answer: B.
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If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink] New post   06 Nov 2017, 12:23
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Bunuel wrote:
If a square mirror has a 30-inch diagonal, what is the area of the mirror, in inches?

A. 225
B. 450
C. 600
D. 750
E. 900

Kudos for correct solution.

Given a square's diagonal, we need side lengths to calculate area.

The relationship between a square's side, s, and its diagonal, d,* is given by

\(s\sqrt{2} = d\)
\(s = \frac{d}{\sqrt{2}}\)

The side of square (d = 30), therefore, is \(\frac{30}{\sqrt{2}}\).

Leave it; no need to rationalize the denominator because it needs to be squared. Square the side length to find area:

\((\frac{30}{\sqrt{2}}\) * \(\frac{30}{\sqrt{2}})\) = \(\frac{30*30}{2}\) = \(\frac{900}{2}=450\)

Answer B

*Although \(d = s\sqrt{2}\) probably should be in memory, it is easily derived. Two sides, \(s\), of a square, form a right isosceles triangle. Pythagorean theorem hence yields:
\(s^2 + s^2 = d^2\)
\(2s^2 = d^2\)
\((\sqrt{2})(\sqrt{s^2})=\sqrt{d^2}\)
\((\sqrt{2})s\\
= d\), or \(s\sqrt{2}= d\)
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Re: If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink] New post   08 Nov 2017, 17:30
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Bunuel wrote:
If a square mirror has a 30-inch diagonal, what is the area of the mirror, in inches?

A. 225
B. 450
C. 600
D. 750
E. 900


Since the diagonal of a square is 30:

diagonal = side√2

30 = side√2

Squaring the entire equation, we have:

30^2 = side^2 x 2

900/2 = side^2

450 = side^2 = area

Answer: B
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Re: If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink] New post   09 Nov 2017, 09:09
Area = (diag 1)* (diag 2)/2

so, Area of the mirror = 30*30/2= 450 sq inch
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Re: If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink] New post   12 Jul 2018, 01:48
s²+s² = 30²

2s² = 900

s² = 450 = the answer
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Re: If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink] New post   03 Feb 2021, 09:16
It's easier if you use the formula for the area of the rhombus (d1*d2/2). A square is a rhombus with diagonals of the same length, then:
A = (30in)(30in)/2 = 450 in²

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Re: If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink]
03 Feb 2021, 09:16
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