Brent@GMATPrepNow wrote: ↑

Thu Apr 09, 2020 7:25 am

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

A) 3√3
B) 6
C) 8
D) 6√2
E) 4√3

Answer: C
Source: www.gmatprepnow.com

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° [since angles in a triangle add to 180°]
So, we now know that triangle PTS is an equilateral triangle
We get:


Area of equilateral triangle [(√3)/4](side²)
Since we're told the area of ∆PTS = √12, we can write: [(√3)/4](x²)=√12
Multiply both sides by 4 to get: (√3)(x²)=4√12
Divide both sides by √3 to get: x² = (4√12)/(√3)
Simplify numerator: x² = (8√3)/(√3)
Simplify : x² = 8
Since the area of square PQRS = x², we know that the area of square PQRS is 8

Answer: C

Cheers,
Brent