If the sides of an equilateral triangle are given by 2a−b−3,a−b+1 and 2a−2b−1, then the perimeter (in cms) of the triangle is
A
6
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B
9
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C
12
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D
15
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Solution
The correct option is C 9 Since the triangle is equilateral, therefore 2a−b−3=a−b+1=2a−2b−1 ⇒(2a−b−3)−(a−b+1)=0 and (2a−b−3)−(2a−2b−1)=0 ⇒a−4=0,b−2=0 ∴a=4 or b=2 These values give 2a−b−3=2×4−2−3=3, so that each side is 3 cm. ∴ Perimeter =3×3=9 cm.