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  • The perimeter of an equilateral triangle is 60 m. The area is (A) 10sqrt{3} m^{2} (B) 15sqrt{3} m^{2} (C) 20sqrt{3}\;m^{2} (D) 100sqrt{3} m^{2}

The perimeter of an equilateral triangle is 60 m. The area is

(A) 10\sqrt{3}\; m^{2}

(B) 15\sqrt{3}\; m^{2}

(C) 20\sqrt{3}\; m^{2}

(D) 100\sqrt{3}\; m^{2}

Answers (1)

[D]

Given perimeter of equilateral triangle = 60 m

Suppose the sides of equilateral triangle, AB = BC = CA = x m

We know that the perimeter of an equilateral triangle = 3 × side

60 = 3 × x

60 = 3x

\frac{60}{3}\; = x

x = 20 m

i.e., sides AB = BC = CA = 20 m

We know that

Area of equilateral triangle  = \frac{\sqrt{3}}{4}\; \times \; side^{2}

\frac{\sqrt{3}}{4}\; \times \; \left ( 20 \right )^{2}\; = \frac{\sqrt{3}}{4}\; \times \;20\times \; 20

= \sqrt{3} × 5 × 20 = \sqrt{3} × 100 = 100\sqrt{3}\; m^{^{2}}

Hence the area of an equilateral triangle is 100\sqrt{3}\; m^{^{2}}.

Hence option (D) is correct.

 

Posted by

infoexpert21

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