Question

On the staircase shown above, both the depth and the height of each step are s, and each step forms a right angle. What is the value of t in terms of s?

• A. $10s$
• B. $14s$
• C. $7s\sqrt{2}$
• D. $7s\sqrt{3}$

Answer 1

The correct option is C $7s\sqrt{2}$

In $△ABC$, $\angle A={90}^o$

By Pythagoras theorem,

$B{C}^2=A{C}^2+A{B}^2$

$B{C}^2=s^2+s^2=2s^2$

So, $BC=s\sqrt{2}$

Now, $t=7\times BC$

Hence, $t=7s\sqrt{2}$