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08 Jun 2022, 02:45
Kudos
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A
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Difficulty:
35%
(medium)
Question Stats:
64% (01:31) correct
36%
(02:40)
wrong
based on 22
sessions
History
Date
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Not Attempted Yet
If the ratio of the heights of two equilateral triangles is 3/2, what is the ratio of the area of the larger triangle to the smaller triangle?
A. 9/4
B. 3/2
C. \(\frac{3\sqrt{3}}{2}\)
D. \(\frac{\sqrt{3}}{2}\)
E. \(\frac{\sqrt{3}}{4}\)
A. 9/4
B. 3/2
C. \(\frac{3\sqrt{3}}{2}\)
D. \(\frac{\sqrt{3}}{2}\)
E. \(\frac{\sqrt{3}}{4}\)
08 Jun 2022, 07:00
Kudos
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Bunuel
Let's make the height of the taller triangle \(3\sqrt{3}\) and the height of the smaller triangle \(2\sqrt{3}\).
Now, let's cut each triangle in half to make 30-60-90s. Half of the base of the larger triangle is 3, and half the base of the smaller triangle is 2.
Area of larger triangle is \(9\sqrt{3}\). Area of smaller triangle is \(4\sqrt{3}\).
The ratio of their areas is 9:4.
Answer choice A.
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