Question

If 2x – 3y + 1, x + y – 1 and 3x – y – 9 denote the three sides of an equilateral triangle.

Find its perimeter.

• A. 14 cm
• B. 21 cm
• C. 28 cm
• D. 35 cm

Answer 1

The correct option is B

21 cm

$\text{Since, all sides are equal}\therefore 2x-3y+1=x+y-1x-4y=-2...............\left(i\right)Also,x+y-1=3x-y-9\Rightarrow x-3x+y+y=-8\Rightarrow -2x+2y=-8\Rightarrow x-y=4..................\left(ii\right)\text{On subtracting (ii) from (i), we get}-3y=-6\Rightarrow y=2\text{On substituting y=2, in (ii), we have}x-2=4\Rightarrow x=6Thereforeside=2x-3y+1=2\times 6-3\times 2+1=6+1=7cm\text{and perimeter}=3\times side=21cm.$