Question

What is the perimeter of $△$ ADE given in the figure?

• A. 8 + $4\sqrt{2}$ cm
• B. 12 + $4\sqrt{3}$ cm
• C. 8 + $4\sqrt{3}$ cm
• D. 4 + $4\sqrt{3}$ cm

Answer 1

The correct option is B

12 + $4\sqrt{3}$ cm

Perimeter of $△$ ADE = AD + DE + AE

AC = $\sqrt{A{B}^2+B{C}^2}$

AC = $\sqrt{4^2+4^2}$ = $\sqrt{32}$ = $4\sqrt{2}$ cm

AD = $\sqrt{A{C}^2+C{D}^2}$

AD = $\sqrt{(4\sqrt{2}{)}^2+4^2}$ = $\sqrt{48}$ = $4\sqrt{3}$ cm

AE = $\sqrt{A{D}^2+D{E}^2}$

AE = $\sqrt{(4\sqrt{3}{)}^2+4^2}$ = $\sqrt{64}$ = 8 cm

$\therefore$ Perimeter of $△$ ADE = AD + DE + AE

= $4\sqrt{3}$ + 4 + 8

= 12 + $4\sqrt{3}$ cm