Question : If the sides of an equilateral triangle are increased by 1 metre, then its area is increased by $\sqrt3$ sq. metre. The length of any of its sides is:
Option 1: $2$ metres
Option 2: $\frac{5}{2}$ metres
Option 3: $\frac{3}{2}$ metres
Option 4: $\sqrt3$ metres
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Correct Answer: $\frac{3}{2}$ metres
Solution :
Given: If the sides of an equilateral triangle are increased by 1 metre, then its area is increased by $\sqrt3$ sq. metre.
Let the sides of the equilateral triangle be $a$ metre.
We know that, the area of the equilateral triangle = $\frac{\sqrt3}{4}a^2$
According to the question,
$\frac{\sqrt3}{4}(a+1)^2-\frac{\sqrt3}{4}a^2 = \sqrt3$
⇒ $(a+1)^2-a^2 = \sqrt3×\frac{4}{\sqrt3}$
⇒ $a^2+2a+1-a^2 = 4$
⇒ $2a=3$
$\therefore a=\frac{3}{2}$
Hence, the correct answer is $\frac{3}{2}$ metres.
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