Question

A ladder is leaning against a wall. The top of the ladder is 9 feet above the ground. If the bottom of the ladder is moved 3 feet farther from the wall, the ladder will be lying flat on the ground, still touching the wall. How long, in feet, is the ladder?

Answer 1

the ladder is l
distance from top is h.
distance from bottom of ladder is r.
By using Pythagoras theorem
$l {}^{2} = {h}^{2} + r {}^{2} \\ {l}^{2} = 9 {}^{2} + {3}^{2} \\ {l}^{2} = 81 + 9 \\ {l}^{2} = 90 \\ l = \sqrt{90 } \\ l = 9.4$
so the length of ladder is 9.4 feet.

Answer 2

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

$\green{\therefore{\text{Length\:of\:ladder=9.48\:feet}}}$

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

• In the given question information given about a ladder is leaning against a wall. The top of a ladder is 9 feet off the floor and the base of the ladder is 3 feet away from the wall.

• We have to find the Length of ladder.

$\green{\underline \bold{Given :}} \\ : \implies \text{Height\:of\:wall=9\:feet} \\ \\ : \implies \text{Distance\:between\:wall\:and\:foot\:of\:ladder=3\:feet}\\\\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Length\:of\:ladder= ?}$

• Accroding to given question :

$\bold{ By \: pythagoras \: theorem} \\ : \implies {h}^{2} = {p}^{2} + {b}^{2} \\ \\ : \implies {AC}^{2} = {AB}^{2} + {BC}^{2} \\ \\ : \implies {AC}^{2} = {9}^{2} + 3^{2} \\ \\ : \implies {AC}^{2} =81+9\\ \\ : \implies {AC}^{2} =90 \\ \\ : \implies AC= \sqrt{90} \\ \\ \green{: \implies \text{AC = 9.48\: feet}}$