GATE 2018 IN GA Q.4: solution and answer

GATE 2018 · INGA Q.4 · 1 mark · MCQ

The area of an equilateral triangle is $3$ . What is the perimeter of the triangle?

(A)
2
(B)
4
(C)
6
(D)
8

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Answer and solution

ANSWER

The side is 2, so the perimeter is 6. Option (C).

Official answer: CSource: Official answer key, GATE 2018 IN (IIT Guwahati)

For an equilateral triangle of side $a$ , the area is $A = \frac{3}{4} a^{2}$ .
Set this equal to the given area: $\frac{3}{4} a^{2} = 3$ .
Divide both sides by $3$ to get $\frac{a ^{2}}{4} = 1$ , so $a^{2} = 4$ and $a = 2$ . Take the positive root because a length cannot be negative.
All three sides of an equilateral triangle are equal, so the perimeter is $3 a = 3 \times 2 = 6$ .
Check: $\frac{3}{4} (2)^{2} = \frac{4 3}{4} = 3$ , which matches the given area. The answer is (C) 6.

KEY IDEA

The area of an equilateral triangle depends only on its side: $A = \frac{3}{4} a^{2}$ . Solve this for $a$ , then multiply by 3 to get the perimeter.

WATCH OUT FOR

Stopping at the side length, which gives $a = 2$ and wrongly picks (A) 2. Another mistake is using $A = \frac{3}{2} a^{2}$ (mixing up the altitude $\frac{3}{2} a$ with the area). That gives $a = 2$ , and the perimeter $32$ is not among the options.

From the GATE 2018 IN paper. Every question of this paper · Download the full paper · All 22 Geometry questions, with notes

GATE 2018 IN GA Q.4: solution and answer

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