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![Quadrilateral ABCD is composed of four 30–60–90 triangles. If \(BD=10\](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "Quadrilateral ABCD is composed of four 30–60–90 triangles. If \(BD=10\"){kind=icon}
26 Mar 2021, 05:00
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B
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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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26 Mar 2021, 05:06
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Bunuel
It makes ∆ABC and BCD both equilateral triangles
Now, BD = 2*Height of one equilateral triagle \(= 2*\frac{√3}{2}*Side = 10√3\)
i.e. \(Side = 10\)
\(Perimeter = 4*10 = 40\)
Answer: Option B
26 Mar 2021, 05:29
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let us consider two diagonals intersect at point O; as we know in 30,60, 90 degree triangle sides are in the ratio 1:sqrt3:2
using triangle OAD (30,60 and 90 degree angle triangle) we know because of symmetry OD=5*sqrt3, so AD=5*sqrt3*2/Sqrt3=10
Perimeter=4*AD=4*10=40
using triangle OAD (30,60 and 90 degree angle triangle) we know because of symmetry OD=5*sqrt3, so AD=5*sqrt3*2/Sqrt3=10
Perimeter=4*AD=4*10=40
