Question

Distance between two parallel lines is unity. A point P lies between the lines at a distance 'a' from one of them. Find the length of a side of an equilateral triangle PQR such that Q lies on one of the parallel lines while R lies on the other.

• A. $\frac{2}{\sqrt{3}}\sqrt{a^3-a^2+1}$
• B. $\frac{2}{\sqrt{3}}\sqrt{a^2-a}+1$
• C. $\frac{2}{\sqrt{3}}\sqrt{a^2-a+1}$
• D. $\frac{2}{\sqrt{3}}\sqrt{a^3-a^2}+1$

Answer 1

The correct option is C $\frac{2}{\sqrt{3}}\sqrt{a^2-a+1}$

10.Let x be the length of the side of the equilateral triangle PQR (see fig.).