Question

A ladder reaches a wall upto a height of 16m and the foot of the ladder 8m away
from the base of the wall find the length of ladder

Answer 1

Height of the wall be h
Distance from the foot of the ladder and wall be x
Let the ladder length be l

From Pythagoras theorem
${h}^{2} + {x}^{2} = {l}^{2}$
${16}^{2} + {8}^{2} = {l }^{2}$
$l = \sqrt{320}$
$l = \sqrt{16 \times 20}$
$l = 4 \sqrt{20}$
$l = 8 \sqrt{5} m$

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Length\:of\:ladder=17.88\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about a ladder reaches a wall upto a height of 16m and the foot of the ladder 8m away from the base of the wall

• Wh have to find the length of ladder.

$\green{\underline \bold{Given :}} \\ : \implies \text{Distance\:between\:wall\:and\:foot\:of\: ladder= 8\: m} \\ \\ : \implies \text{Heigh\:of\:wall= 16\:m} \\ \\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Length\:of\: ladder = ?}$

• Accroding to given question :

$\bold{In \: \triangle \: ABC} \\ : \implies {h}^{2} = {p}^{2} + {b}^{2} \: \: \: \: \: \: \: \: \text{(by \: phythagoras \: theoram}) \\ \\ : \implies {(AC)}^{2} = {16}^{2} + {8}^{2} \\ \\ : \implies (AC)^{2} =256+64\\ \\ : \implies {(AC)}^{2} =320 \\ \\ : \implies AC = \sqrt{320} \\ \\ \green{: \implies \text{AC=17.88\:m}}$