Question

the foot of a ladder is 15 metre away from a wall and its top reaches a window 20 m high.find the length of a ladder?​

Answer 1

Let AC is the height of window from ground,

BC is the distance of ladder from the wall

and AB is the Length of the ladder

it is from a right angled triangle, here

• AC = altitude = 20 m
• BC = base = 15 m
• AB = hypotenuse = x m

and now, by using Pythagoras theorem

$\bold{ : \implies {AC}^{2} = {BC}^{2} + {AB}^{2}} \\ \\ \bold{: \implies {x}^{2} = {15}^{2} + {20}^{2} } \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies {x}^{2} = 225 + 400} \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies {x}^{2} = 625 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = \sqrt{625} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = 25 \: m} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence, Length of the ladder is 25 m