Question

What is the perimeter of the square ACEF?

• A. $2\sqrt{2}$ units
• B. $4\sqrt{2}$ units
• C. 4 units
• D. 2 units

Answer 1

The correct option is B

$4\sqrt{2}$ units

To find the Perimeter of square ACEF, we need to know the side.

There are 2 ways to find the side -

Method 1 :

AC = $\sqrt{A{D}^2+C{D}^2}$ = $\sqrt{1^2+1^2}$ = $\sqrt{2}$ units

Method 2 :

AE = 2 cm and AFE is a right angled isosceles triangle with AF = FE

The sides are in the ratio 1 : 1 : $\sqrt{2}$

Let AF = FE = x and AE = $\sqrt{2}$x

$\sqrt{2}$x = 2

x = $\sqrt{2}$

$\Rightarrow$ AF = FE = $\sqrt{2}$ units

$\therefore$ Perimeter of the square = 4 $\times$ Side = $4\times \sqrt{2}$ = $4\sqrt{2}$ units