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Joined: 10 Apr 2015
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In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS
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09 Apr 2020, 07:24
09 Apr 2020, 07:24
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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
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Joined: 30 Mar 2020
Posts: 27
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WE:Research (Health Care)
Re: In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS
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10 Apr 2020, 00:19
10 Apr 2020, 00:19
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Answer: 8
Triangle PTS is an equilateral triangle.
Lets split triangle PTS into x:x√3:2x
PS=X
PS/2=X/2
X√3=x√3/2
√12=X*√3/2 *1/2
√12=X2√3/4
4√12=X2√3
4√3√4=X2√3
4√4=X2
8=X2
√8=X
Area of Square: PS * QP = √8 * √8 = 8
Triangle PTS is an equilateral triangle.
Lets split triangle PTS into x:x√3:2x
PS=X
PS/2=X/2
X√3=x√3/2
√12=X*√3/2 *1/2
√12=X2√3/4
4√12=X2√3
4√3√4=X2√3
4√4=X2
8=X2
√8=X
Area of Square: PS * QP = √8 * √8 = 8
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS
[#permalink]
10 Apr 2020, 05:13
10 Apr 2020, 05:13
1
GreenlightTestPrep wrote:
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
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
