Question

A ladder is placed against a wall in such a way that its foot is at a distance of 9 from the wall and its top reaches a window 12 m above the ground in the wall. Find the length of the ladder.
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Answer 1

15 m is the correct answer

Answer 2

let the length of the ladder be AB = x

and BC is the distance from the wall & AC is the distance of window from the ground

• AB = x
• BC = 9m
• AC = 12m

now, in right angled triangle ABC

we use Pythagoras theorem

• (AB)² = (BC)² + (AC)²

$\bold{ : \implies {x}^{2} = {(9)}^{2} + {(12)}^{2} } \\ \\ \bold{ : \implies {x}^{2} = 81 + 144 } \: \: \: \: \: \: \\ \\ \bold{: \implies {x}^{2} = 225 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = \sqrt{225} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = 15 \: m} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence, Length of the ladder is 15 m