Question

A plank 6m long leans against a vertical wall so that the foot of the plank is 4m away from the wall. A lizard climbs 2m up the plank. Calculate the horizontal distance between the lizard and the wall.

Answer 1

Answer: $\dfrac{8}{3}\ m$

Step-by-step explanation:

Given

Length of the plank is $6\ m$

Foot of the flank is $4\ m$ away from the wall

Lizard climbs 2 m up the wall

from the figure, the two triangles are similar

$\therefore \dfrac{2}{6}=\dfrac{x}{4}\\\\\Rightarrow x=4\times \dfrac{2}{6}\\\\\Rightarrow x=\dfrac{4}{3}\ m$

So, the distance from the wall is

$\Rightarrow 4-x\\\\\Rightarrow 4-\dfrac{4}{3}\\\\\Rightarrow \dfrac{8}{3}\ m$