Question

A piece of wire 132 dm long is bent successively in the shape of an equilateral triangle a square a regular hexagon and a circle Then the area included is largest when the shape is

• A. triangle
• B. square
• C. hexagon
• D. circle

Answer 1

The correct option is D circle

Given the length of wire is 132 dm

If is shape is equilateral triangle Then =$132=\frac{\sqrt{3}}{4}{s}^2\Rightarrow s^2=\frac{4\times 132}{\sqrt{3}}\Rightarrow s=13.26$ dm

If it is bend in square then =$6s^2=132\Rightarrow s^2=22\Rightarrow s=4.70dm$

IF it bis bend in regular hexagon then =$\frac{3\sqrt{3}{s}^2}{2}=132\Rightarrow s^2=88\sqrt{3}\Rightarrow s=9.8$ dm

If it is bend in circle then =$\pi s^2=132\Rightarrow s^2=\frac{7\times 132}{22}\Rightarrow s=4.69$ dm

Then side of triangle is largest then equilateral triangle is largest in shape