Question

A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder. [3 MARKS]

Answer 1

Formula: 1 Mark
Steps: 1 Mark
Result: 1 Mark

Let AB be the ladder and CA be the wall with the window at A.

Given, BC = 2.5 m and CA = 6 m



Since wall and window are perpendicular to each, applying Pythagoras Theorem, we have:

${AB}^2={BC}^2+{CA}^2$

${AB}^2={\left(2.5\right)}^2+{\left(6\right)}^2$

${AB}^2=6.25+36$

${AB}^2=42.25$

$\Rightarrow AB=6.5$

Thus, length of the ladder is 6.5 m.