Question

ABC is an equilateral triangle and AX,BY and CZ are three parallel lines. Find the area of triangle ABC

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

There is no constraint given, other than that ABC is an equilateral triangle and AX || BY || CZ.
We can therefore assume that X,Y and Z are points on the side AC itself. If we assume the equilateral triangle to have a side=2, and the Y is the mid point of AC, then AY=YB=1
Area of the triangle = $\frac{\sqrt{3}}{4}$ $a^2$ = $\sqrt{3}$
Look in the answer options and eliminate those options where you do not get √3 on substituting a=1 and b=1.

Answer is option (b)