Question

XYZ is an equilateral triangle and PQRS is a square. The figure has been cut and rearranged in the form of a trapezium.

What is the Perimeter of the rectangle ABCD? ( $△$ XYZ is equilateral )

• A. 4(1 + $\sqrt{3}$) cm
• B. 8(1 + $\sqrt{3}$) cm
• C. 6(1 + $\sqrt{3}$) cm
• D. 8(1 + $\sqrt{2}$) cm

Answer 1

The correct option is B

8(1 + $\sqrt{3}$) cm

To know the perimeter of the rectangle we need to know the following Lengths :

AB , BC , CD and AD

AB = CD = Height of the equilateral triangle with side 8 cm

Using Pythagoras theorem,

AB = $\sqrt{8^2-4^2}$

= $\sqrt{48}$ cm

BC = AD = 4 cm (Side of Square)

$\therefore$ Perimeter of the given rectangle ABCD = AB + BC + CD + AD

= $\sqrt{48}$ + 4 + $\sqrt{48}$ + 4

= $2\sqrt{48}$ + 8

= $8\sqrt{3}$ + 8

= 8(1 + $\sqrt{3}$) cm