Question

In the figure above, $CDE$ is an equilateral triangle and $ABCE$ is a square with an area of $1$. What is the perimeter of polygon $ABCDE$?

• A. 4
• B. 5
• C. 6
• D. 7
• E. 8

Answer 1

Answer: (B)

As $△$$CDE$ is equilateral,

let $CD$ $=$ $DE$ $=$ $EC$ $=$ $x$

As $ABCE$ is a square and $CE$ $=$ $x$,

$\Rightarrow EC$ $=$ $BC$ $=$ $BA$ $=$ $AE$ $=$ $x$

Given, Area of the square $ABCE$ $=$ $1$

$\Rightarrow x^2$ $=$ $1$

$\Rightarrow x$ $=$ $1$

Perimeter of the polygon $ABCDE$ $=$ $AB$ $+$ $BC$ $+$ $CD$ $+$ $DE$ $+$ $EA$

$=$ $x$ $+$ $x$ $+$ $x$ $+$ $x$ $+$ $x$

$=$ $5x$

$=$ $5$ $\times$ $x$

$=$ $5$ $\times$ $1$

$=$ $5$

Therefore, perimeter of the polygon $ABCDE$ is ${}^{\prime }{5}^{\prime }$.