Question

A ladder is lying against a wall which is 5 meters high. If the ladder slips 2 meters away from the wall, the top of the ladder touches the foot of the wall. The length of the ladder is

Answer 1

Answer:

Length of ladder = 7.25 m

Step-by-step explanation:

there can be two cases here

case 1

ladder slips 2 meters away from the wall

then 2 meter is the ladder length as ladder is touching foot of wall so lying horizontally.

Ladder Length = 2m

Case 2

Ladder slips 2 m further away from the wall and was earlier touching top of wall

then let say length of ladder = L m

then earlier it was away from wall = L - 2 m

L² = (L  -2)² + 5²

=> L² = L² + 4 - 4L + 25

=> 4L = 29

=> L = 7.25 m

Length of ladder = 7.25 m

Answer 2

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

$\green{\therefore{\text{Length\:of\:ladder=7.25\:m}}}$

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

• In the given question information given about a ladder lies against a wall. The top of the ladder reaches 5 m above the ground. When the ladder slips by 2 m away from the wall, the top of the ladder touches the foot of the wall.

• We have to find the length of the ladder.

$\green{\underline \bold{Given :}} \\ : \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} = {5}^{2} + {x}^{2} \\ \\ : \implies {x}^{2} + 4 + 4x = {x}^{2} + 25 \\ \\ : \implies {x}^{2} - {x}^{2} + 4x = 25-4 \\ \\ : \implies x = \frac{21}{4} \\ \\ \green{: \implies \text{x = 5.25\: m}}\\\\\green{\therefore \text{length\:of\:ladder=5.25+2=7.25\:m}}$