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A puzzle board is in the form of an equilateral triangle that has an a
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29 Jan 2025, 13:12
29 Jan 2025, 13:12
Expert Reply
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Question Stats:
66% (02:00) correct
33% (01:48) wrong based on 6 sessions
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A puzzle board is in the form of an equilateral triangle that has an area of $7√3$ square inches. If the puzzle board is placed on a circular table, what should be the minimum area of the table so that whole of the board fits inside the table?
(A) 30
(B) $883$
(C) 22
(D) $443$
(E) 11
(A) 30
(B) $883$
(C) 22
(D) $443$
(E) 11
A puzzle board is in the form of an equilateral triangle that has an a
[#permalink]
05 Mar 2025, 13:30
05 Mar 2025, 13:30
Expert Reply
Area of the equilateral triangle is $\frac{\sqrt{3{4} \times$ Side $2=7√3⇒$ Side $=√28=2√7$
The radius of the circle which circumscribes an equilateral triangle of side ' $a$ ' units is $\frac{a}{\sqrt{3$ (= circum-radius), so, the radius of the circle which would circumscribe an equilateral triangle of side $2√3$ would be $2√7√3=2√73$
So, the area of the circular table would be $\pi r^2=\frac{22}{7} \times\left(2 \sqrt{\frac{7}{3\right)^2=\frac{88}{3}$
Hence the answer is (B).
The radius of the circle which circumscribes an equilateral triangle of side ' $a$ ' units is $\frac{a}{\sqrt{3$ (= circum-radius), so, the radius of the circle which would circumscribe an equilateral triangle of side $2√3$ would be $2√7√3=2√73$
So, the area of the circular table would be $\pi r^2=\frac{22}{7} \times\left(2 \sqrt{\frac{7}{3\right)^2=\frac{88}{3}$
Hence the answer is (B).
gmatclubot
A puzzle board is in the form of an equilateral triangle that has an a [#permalink]
05 Mar 2025, 13:30
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