Question

From an equilatera triangular plate of side ${}^{\prime }{a}^{\prime }$, a square plate of maximum size has to be cut. THe side of such a square plate is:

• A. $\frac{\sqrt{3}a}{2}$
• B. $\frac{(2+\sqrt{3})a}{2}$
• C. $\frac{(1+\sqrt{3})a}{8}$
• D. $\frac{\sqrt{3}a}{2+\sqrt{3}}$

Answer 1

The correct option is D $\frac{\sqrt{3}a}{2+\sqrt{3}}$



Let the side of the square plate of maximum size be $x$.
For $\Delta ACD$
$\frac{\frac{\sqrt{3}}{2}a-x}{x/2}=tan60$
$\frac{\sqrt{3}a-2x}{x}=\sqrt{3}$
$x=\frac{\sqrt{3}a}{(2+\sqrt{3})}$