In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS = √12,

Question

https://i.imgur.com/lcjgngY.png

In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS = √12, what is the area of square PQRS?

A) 3√3
B) 6
C) 8
D) 6√2
E) 4√3

nick1816 · Answer

∠TPS = ∠TSP = 90-30=60

PTS is an equilateral triangle. Assume PS= 'a'

\frac{\sqrt{3}}{4} *a^2 =√12 = 2√3

a^2 = 8

preetamsaha · Answer

∠QPT = ∠RST = 30°.
∠TPS = ∠TSP = 90°-30°=60°
so,PTS is an equilateral triangle.
let, the side of the triangle = x
therefore, √3/4 *x^2 = √12
or, x^2= 8
therefore, area of the square is 8 
 correct answer is C

BrentGMATPrepNow · Answer

Since we're told PQRS is a SQUARE, we know that all 4 angles are 90 degrees. 
So, if ∠QPT = ∠RST = 30°, then the two other angles are each   60°  
If two of the angles in the triangle   60°   each, then the third angle must also be   60°      
So, we now know that triangle PTS is an  equilateral triangle 
We get: 
 https://i.imgur.com/0iPkVi7.png

Area of equilateral triangle  = \frac{\sqrt{3}}{4}(side)^2

Since we're told the area of ∆PTS = √12, we can write:  \frac{\sqrt{3}}{4}(x^2)=\sqrt{12}

Multiply both sides by  4  to get:  \sqrt{3}(x^2)=4\sqrt{12}

Divide both sides by  \sqrt{3}  to get:  x^2=\frac{4\sqrt{12}}{\sqrt{3}}

Simplify numerator:  x^2=\frac{8\sqrt{3}}{\sqrt{3}}

Simplify :  x^2=8

Since the area of square PQRS  = x^2 , we know that the area of square PQRS is  8

Answer: C

Cheers,
Brent

In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS = √12,

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In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS = √12,

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards