Question

What is the ratio between AE and AF if EF = 1m ?

• A. 1 : $\sqrt{5}$
• B. 2 : $\sqrt{5}$
• C. $\sqrt{5}$ : 3
• D. 1 : $\sqrt{3}$

Answer 1

The correct option is B

2 : $\sqrt{5}$

We have AB = BC = CD = DE = EF = 1 m

To find AE , we need to find AC, and then AD using Pythagoras theorem.

AC = $\sqrt{1^2+1^2}$ = $\sqrt{2}$ m

AD = $\sqrt{1^2+(\sqrt{2}{)}^2}$ = $\sqrt{1+2}$ = $\sqrt{3}$ m

$\therefore$ AE = $\sqrt{1^2+(\sqrt{3}{)}^2}$ = $\sqrt{1+3}$ = 2 m

$\therefore$ AF = $\sqrt{1^2+2^2}$ = $\sqrt{5}$ m

Ratio between AE and AF = 2 : $\sqrt{5}$