Question

A ladder is leaning against a wall. The top of a ladder is 5m off the floor and the base of the ladder is 1m away from the wall.

How long is the ladder? Give your answer to one decimal place.

Answer 1

By Pythogaras,

height of ladder = √5²+1²

                            = √25+1 = √26

                            = 5.09 m

Answer 2

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

$\green{\therefore{\text{Length\:of\:ladder=5.1\:m}}}$

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

• In the given question information given about a ladder is leaning against a wall. The top of a ladder is 5m off the floor and the base of the ladder is 1m away from the wall.

• We have to find the Length of ladder.

$\green{\underline \bold{Given :}} \\ : \implies \text{Height\:of\:wall=5\:m} \\ \\ : \implies \text{Distance\:between\:wall\:and\:foot\:of\:ladder=1\:m}\\\\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Length\:of\:ladder= ?}$

• Accroding to given question :

$\bold{ By \: pythagoras \: theorem} \\ : \implies {h}^{2} = {p}^{2} + {b}^{2} \\ \\ : \implies {AC}^{2} = {AB}^{2} + {BC}^{2} \\ \\ : \implies {AC}^{2} = {5}^{2} + 1^{2} \\ \\ : \implies {AC}^{2} =25+1\\ \\ : \implies {AC}^{2} =26 \\ \\ : \implies AC= \sqrt{26} \\ \\ \green{: \implies \text{AC = 5.1\: m}}$