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PQR and STU are two identical equilateral triangles. Triangle SWV has

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PQR and STU are two identical equilateral triangles. Triangle SWV has [#permalink] New post   30 Sep 2021, 10:45
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PQR and STU are two identical equilateral triangles. Triangle SWV has a perimeter of 9 and PQ is 6.

Quantity A
Quantity B
Perimeter of polygon PQWTUVR
27


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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C
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void
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Re: PQR and STU are two identical equilateral triangles. Triangle SWV has [#permalink] New post   01 Oct 2021, 11:01
solution please.
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Re: PQR and STU are two identical equilateral triangles. Triangle SWV has [#permalink] New post   01 Oct 2021, 14:15
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void wrote:
solution please.

Total perimeter of the two triangles is 6*3+6*3 = 36
Now, we know the perimeter of the small intersecting triangle to be 9.
So, all we have to do is subtract sum of SWV from PQR and STU
36 - 9 = 27
(Think of it like this: SVW is now not included in the sum any longer)
WS+SV+WV are not the part of the perimeter anymore
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Re: PQR and STU are two identical equilateral triangles. Triangle SWV has [#permalink] New post   03 Oct 2021, 00:34
The perimeter of the Polygon = Sum of perimeter of both equilateral triangles - Perimeter of triangle SWV.

Sum of the sides of both equilateral triangles = (total no of sides) * (length of each side) = 6*9 = 36.
Perimeter of the polygon = 36 - 9 = 27.

Since Qnty A = Qnty B. answer is C
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Re: PQR and STU are two identical equilateral triangles. Triangle SWV has [#permalink] New post   27 Oct 2023, 09:37
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void wrote:
solution please.


The solutions given are actually shorter than my method but I'll state it:

So, basically SWV is also an eq triangle (since angle TWV = angle UVW = 120 [WVUT is a trapezium so opp angles are supplementary], so then SWV = SVW = 180 -120 = 60].

Now for the perimeter: PQ + PR + TU + (QR - WV) + (ST - SW) + (SU - SV) = 18 + 3 + 3 + 3 = 27 = B. Answer is C
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