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# In square PQRS above, triangle PTS has a perimeter of 30. What is the

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Math Expert
Joined: 02 Sep 2009
Posts: 64181
In square PQRS above, triangle PTS has a perimeter of 30. What is the  [#permalink]

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24 Feb 2019, 23:06
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15% (low)

Question Stats:

86% (01:02) correct 14% (02:17) wrong based on 35 sessions

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In square PQRS above, triangle PTS has a perimeter of 30. What is the area of square PQRS?

(A) 30

(B) 50

(C) 60

(D) 75

(E) 100

Attachment:

#GREpracticequestion In square PQRS above.jpg [ 11.65 KiB | Viewed 616 times ]

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Re: In square PQRS above, triangle PTS has a perimeter of 30. What is the  [#permalink]

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24 Feb 2019, 23:58
Bunuel wrote:

In square PQRS above, triangle PTS has a perimeter of 30. What is the area of square PQRS?

(A) 30

(B) 50

(C) 60

(D) 75

(E) 100

Attachment:
#GREpracticequestion In square PQRS above.jpg

triangle PTS is equilateral
so s= 30/3 ; 10
s^2 = 100; area of square
IMO E
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4876
GMAT 1: 770 Q49 V46
Re: In square PQRS above, triangle PTS has a perimeter of 30. What is the  [#permalink]

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02 Apr 2020, 06:15
Top Contributor
1
Bunuel wrote:

In square PQRS above, triangle PTS has a perimeter of 30. What is the area of square PQRS?

(A) 30
(B) 50
(C) 60
(D) 75
(E) 100
Attachment:
#GREpracticequestion In square PQRS above.jpg

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:

Given: triangle PTS has a perimeter of 30
All sides in an equilateral triangle have equal lengths, we can write: x + x + x = 30
Solve, to get: x = 10

This also means that each side of square PQRS has length 10
Area of square = (side)² = 10² = 100

Cheers,
Brent
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Re: In square PQRS above, triangle PTS has a perimeter of 30. What is the   [#permalink] 02 Apr 2020, 06:15

# In square PQRS above, triangle PTS has a perimeter of 30. What is the

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