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In triangle ABC, AB = AC and angle A = 60o. A semicircle with diamet
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17 Feb 2025, 01:12
17 Feb 2025, 01:12
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In triangle ABC, AB = AC and angle A = 60°. A semicircle with diameter along the side BC is drawn. If length of the arc of the semi-circle is 50π, what is the perimeter of the triangle?
A. 100
B. 200
C. 300
D. 400
E. 500
A. 100
B. 200
C. 300
D. 400
E. 500
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Re: In triangle ABC, AB = AC and angle A = 60o. A semicircle with diamet
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11 Mar 2025, 11:21
11 Mar 2025, 11:21
Expert Reply
In triangle ABC , angle A is 60 degrees and $\(\mathrm{AB}=\mathrm{AC} \Rightarrow \angle \mathrm{B}=\angle \mathrm{C}=\frac{1}{2}(180-60)=60\)$ (When sides are equal, opposite angles are also equal and the sum of the angles of a triangle is 180 degrees). So, triangle ABC is an equilateral triangle.
Also we are given that a semi circle is drawn with diameter along the side $\(B C\)$, so the radius of the circle, say $\(r\)$, must be half of $\(B C\)$
The length of the arc of the semi circle $\(=\frac{1}{2}(2 \pi r)=\pi r=50 \pi \Rightarrow r=50\)$, so we get $\(B C=\)$ $\(2 \mathrm{r}=2 \times 50=100\)$
Finally, the perimeter of the triangle ABC is $\(3 \times\)$ Side $\(=3 \times 100=300\)$
Hence the answer is (C).
Also we are given that a semi circle is drawn with diameter along the side $\(B C\)$, so the radius of the circle, say $\(r\)$, must be half of $\(B C\)$
The length of the arc of the semi circle $\(=\frac{1}{2}(2 \pi r)=\pi r=50 \pi \Rightarrow r=50\)$, so we get $\(B C=\)$ $\(2 \mathrm{r}=2 \times 50=100\)$
Finally, the perimeter of the triangle ABC is $\(3 \times\)$ Side $\(=3 \times 100=300\)$
Hence the answer is (C).
gmatclubot
Re: In triangle ABC, AB = AC and angle A = 60o. A semicircle with diamet [#permalink]
11 Mar 2025, 11:21
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