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Two congruent triangles were combined in three different ways, as show

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Bunuel
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Two congruent triangles were combined in three different ways, as show [#permalink] Two congruent triangles were combined in three different ways, as show   27 May 2021, 02:00
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Two congruent triangles were combined in three different ways, as shown above. If the perimeters of the shapes above are 12, 14, and 16, then what is the perimeter of one triangle?

A. 13/2
B. 14/2
C. 21/2
D. 22/2
E. 42/3

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Re: Two congruent triangles were combined in three different ways, as show [#permalink] Two congruent triangles were combined in three different ways, as show   27 May 2021, 02:24
can someone pls provide an explanation to this question. according to me the answer should be option E.
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Re: Two congruent triangles were combined in three different ways, as show [#permalink] Two congruent triangles were combined in three different ways, as show   27 May 2021, 02:40
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Assume the sides of the triangle are a,b, & c

The perimeter of three different quadrilaterals will be

2a+2b = 12
2b+2c = 14
2c+2a = 16

Solve for a or b or c and add it with one of the above equation for perimeter.

Ans = C
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Two congruent triangles were combined in three different ways, as show [#permalink] Two congruent triangles were combined in three different ways, as show   27 May 2021, 02:49
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Using the rectangle we can see that we have 3 different sides making up the triangle. Let the breadth be x, length be y and the diagonal be z.

All 3 of the shapes' perimeters are comprised of 2 sets of 2 of these (each shape having 4 sides in total).

Rectangle: 2(x+y) = 12
x+y = 6

Diamond shape under the rectangle: 2(z+y) = 14
z+y = 7

Mirrored triangles to the right of the rectangle: 2(z+x) =16
z+x = 8


Summing these together we get: x+y+z+y+z+x = 6+7+8
2x + 2y + 2z = 21
Now we know that a single triangle's perimeter comprises of x+y+z so we divide through by 2 to get:
x+y+z = 21/2

Answer C
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Re: Two congruent triangles were combined in three different ways, as show [#permalink] Two congruent triangles were combined in three different ways, as show   23 Jun 2023, 11:07
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Re: Two congruent triangles were combined in three different ways, as show [#permalink]
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