If the sides of an equilateral triangle are given by $2 a - b - 3, a - b + 1$ and $2 a - 2 b - 1$ , then the perimeter (in cms) of the triangle is

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Solution

The correct option is C 9
Since the triangle is equilateral, therefore
$2 a - b - 3 = a - b + 1 = 2 a - 2 b - 1$
$\Rightarrow (2 a - b - 3) - (a - b + 1) = 0$
and $(2 a - b - 3) - (2 a - 2 b - 1) = 0$
$\Rightarrow a - 4 = 0, b - 2 = 0$
$∴ a = 4$ or $b = 2$
These values give $2 a - b - 3 = 2 \times 4 - 2 - 3 = 3,$
so that each side is $3$ cm.
$∴$ Perimeter $= 3 \times 3 = 9$ cm.

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