Question

A ladder lies against a wall. The top of the ladder reaches 8 feet above the ground. When the ladder slips by two feet away from the wall, the top of the ladder touches the foot of the wall. The length of the ladder (in feet) is

Answer 1

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

$\green{\therefore{\text{Length\:of\:ladder=17\:feet}}}$

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

• In the given question information given about a ladder lies against a wall. The top of the ladder reaches 8 feet above the ground. When the ladder slips by two feet away from the wall, the top of the ladder touches the foot of the wall.

• We have to find the length of the ladder (in feet).

$\green{\underline \bold{Given :}} \\ : \implies : \implies\text{Heigh\:of\:wall=8\:feet}\\ \\ \red{\underline \bold{To \: Find:}} \\ : \implies\text{Length\:of\: ladder=?}$

$\text{let \: distance \: between \: wall \: and \: ladder \: be \: x} \\ \\ \bold{after \: sliding \: 2 \: m} \\ : \implies \text{distance \: between \: wall \: and \: ladder(bd) =(x + 2)m} \\ \\ : \implies \text{length \: of \: ladder = (x + 2)m} \\ \\ \bold{in \: \triangle \: abc} \\ \\ \text{by \: pythagoras \: theorem} \\ : \implies {h}^{2} = {p}^{2} + {b}^{2} \\ \\ : \implies (x + 2)^{2} = {8}^{2} + {x}^{2} \\ \\ : \implies {x}^{2} + 4 + 4x = {x}^{2} + 64 \\ \\ : \implies {x}^{2} - {x}^{2} + 4x = 64 - 4 \\ \\ : \implies x = \frac{60}{4} \\ \\ \green{: \implies \text{x = 15\: feet}}\\\\\green{\therefore \text{length\:of\:ladder=15+2=17\:feet}}$