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Quadrilateral ABCD is composed of four 30–60–90 triangles.
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26 Feb 2021, 06:00
26 Feb 2021, 06:00
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Quadrilateral ABCD is composed of four 30–60–90 triangles. If \(BD=10\sqrt{3}\), what is the perimeter of ABCD?
A. 38
B. 40
C. 42
D. 46
E. 47
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Quadrilateral ABCD is composed of four 30–60–90 triangles.
[#permalink]
26 Feb 2021, 06:30
26 Feb 2021, 06:30
GeminiHeat wrote:
Attachment:
1.jpg
Quadrilateral ABCD is composed of four 30–60–90 triangles. If \(BD=10\sqrt{3}\), what is the perimeter of ABCD?
A. 38
B. 40
C. 42
D. 46
E. 47
Since we have four 30-60-90 triangles, We can say AC is perpendicular to BD (intersecting at point E - assume)
So, Quad. ABCD can be a rhombus!
Side Diagonal BD will then bisect i.e. BE = DE = \(5\sqrt{3}\)
In triangle AED:
Angle ADE = 30 with side opposite to it as \(x\)
Angle DAE = 60 with side opposite to it as \(\sqrt{3}x\)
Angle AED = 90 with side opposite to it as \(2x\)
Since DE = \(5\sqrt{3}\)
Then, AD = (2)(5) = 10
This is true for all four triangles. So, AB = BC = CD = AD = 10
Therefore the Perimeter = 40
Hence, option D
gmatclubot
Quadrilateral ABCD is composed of four 30–60–90 triangles. [#permalink]
26 Feb 2021, 06:30
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