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Question

If the area of an equilateral triangle is 93 cm2. What is the length of the side of the triangle.


A

8 cm

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B

9 cm

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C

18 cm

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D

6 cm

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Solution

The correct option is D

6 cm


Let the side of the equilateral triangle = a cm.

Semi Perimeter, s = 3a2

sa=3a2a=3a2a2=a2

Now by heron’s formula

Area of the triangle= s(sa)(sb)(sc)

93=3a2×a2×a2×a2

243=3a416

Squaring both sides,
243=3a416

a4=81×16

a=6 cm

Length of the side = 6 cm


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