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What is the area of the right angled triangle shown in the figure abo
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08 Jan 2025, 02:15
08 Jan 2025, 02:15
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Question Stats:
75% (03:23) correct
25% (03:34) wrong based on 4 sessions
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What is the area of the right angled triangle shown in the figure above?
(A) $\(16 \sqrt{3}\)$
(B) 32
(C) $\(32 \sqrt{3}\)$
(D) 48
(E) $\(48 \sqrt{2}\)$
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Re: What is the area of the right angled triangle shown in the figure abo
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18 Feb 2025, 01:57
18 Feb 2025, 01:57
Expert Reply
OFFICIAL EXPLANATION
As shown in the figure above in a triangle having angles $90,60 \& 30$, the corresponding opposite sides are $\(2 \mathrm{a}, \mathrm{a} \sqrt{3} \& \mathrm{a}\)$ respectively.
Using the $\(90,60,30\)$ triangle rule, in the given triangle as the side opposite to 30 degrees is 2 x , we get the side opposite to 60 degrees as $\(\sqrt{3} \times 2 x=2 x \sqrt{3} \&\)$ opposite to that of 90 degrees as $\(2 \times 2 x=4 x\)$, which is same as $\(4 x=x+12 \Rightarrow x=4\)$
So, the area of the triangle $\(=\frac{1}{2} \times\)$ Base $\(\times\)$ Height $\(=\frac{1}{2} \times 2 \mathrm{x} \times 2 \mathrm{x} \sqrt{3}=2 \sqrt{3} \mathrm{x}^2=2 \sqrt{3} \times(4)^2=32 \sqrt{3}\)$
Hence the answer is (C).
As shown in the figure above in a triangle having angles $90,60 \& 30$, the corresponding opposite sides are $\(2 \mathrm{a}, \mathrm{a} \sqrt{3} \& \mathrm{a}\)$ respectively.
Using the $\(90,60,30\)$ triangle rule, in the given triangle as the side opposite to 30 degrees is 2 x , we get the side opposite to 60 degrees as $\(\sqrt{3} \times 2 x=2 x \sqrt{3} \&\)$ opposite to that of 90 degrees as $\(2 \times 2 x=4 x\)$, which is same as $\(4 x=x+12 \Rightarrow x=4\)$
So, the area of the triangle $\(=\frac{1}{2} \times\)$ Base $\(\times\)$ Height $\(=\frac{1}{2} \times 2 \mathrm{x} \times 2 \mathrm{x} \sqrt{3}=2 \sqrt{3} \mathrm{x}^2=2 \sqrt{3} \times(4)^2=32 \sqrt{3}\)$
Hence the answer is (C).
gmatclubot
Re: What is the area of the right angled triangle shown in the figure abo [#permalink]
18 Feb 2025, 01:57
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