Question

The foot of the ladder is 2 m away from a vertical wall. The height of the ladder is 1 /2 m less than the length of the ladder. Find the length of the ladder

Answer 1

CORRECT QUESTION :

The foot of the ladder is 2 m away from a vertical wall. The height of the wall is 1 /2 m less than the length of the ladder. Find the length of the ladder.

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

$\green{\therefore{\text{Length\:of\:ladder=4.25\:m}}}$

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

$\green{\underline \bold{Given :}} \\ : \implies \text{Length \: of \: ladder = 5 \: m} \\ \\ : \implies \text{Height\:of\:wall=Length\:of\:ladder-0.5\:m} \\ \\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Length\:of\: ladder = ?}$

• Accroding to given question :

$\text{Let\:length\:of\:ladder=x\:m}\\\\\text{Height\:of\:wall=(x-0.5)m}\\\\\bold{In \: \triangle \: ABC} \\ : \implies {h}^{2} = {p}^{2} + {b}^{2} \: \: \: \: \: \: \: \: \text{(by \: phythagoras \: theoram}) \\ \\ : \implies {x}^{2} = {(x-\frac{1}{2})}^{2} + {2}^{2} \\ \\ : \implies x^{2} = x^{2}+\frac{1}{4}-x + 4 \\ \\ : \implies 4x^{2} =4x^{2}+1-4x+16 \\ \\ : \implies 4x^{2}-4x^{2}+4x = 17\\ \\ : \implies x= \frac{17}{4} \\ \\ \green{: \implies \text{x= 4.25\:m}}$