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

Question

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 .

TeamGMATIFY · Accepted Answer

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

livio04 · Answer

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.

rhine29388 · Answer

(30/sqrt 2)^2 = 450
Correct answer - B

AbdurRakib · Answer

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

adiagr · Answer

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.

generis · Answer

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

JeffTargetTestPrep · Answer

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

pawai1989 · Answer

Area = (diag 1)* (diag 2)/2

so, Area of the mirror = 30*30/2= 450 sq inch

Burkwoet · Answer

s²+s² = 30²

2s² = 900

s² = 450 = the answer

alexisrakh · Answer

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

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

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