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

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Math Expert
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If a square mirror has a 30-inch diagonal, what is the area of the mir  [#permalink]

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17 Feb 2016, 02:32
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5% (low)

Question Stats:

81% (00:51) correct 19% (01:08) wrong based on 156 sessions

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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

Kudos for correct solution.

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

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17 Feb 2016, 03:10
1
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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If a square mirror has a 30-inch diagonal, what is the area of the mir  [#permalink]

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23 Feb 2016, 03:08
2
1
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.

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]

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09 Apr 2016, 13:35
(30/sqrt 2)^2 = 450
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Re: If a square mirror has a 30-inch diagonal, what is the area of the mir  [#permalink]

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10 Jun 2016, 13:15
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]

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13 Jun 2016, 23:18
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.

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

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06 Nov 2017, 11:23
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:

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

*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]

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08 Nov 2017, 16:30
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

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

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09 Nov 2017, 08:09
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]

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12 Jul 2018, 00:48
s²+s² = 30²

2s² = 900

s² = 450 = the answer
Re: If a square mirror has a 30-inch diagonal, what is the area of the mir &nbs [#permalink] 12 Jul 2018, 00:48
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