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the foot of a ladder is 6m away from a wall and it's top reaches a window 8m above the ground if the ladder is shifted in such a way that it's foot is 8m

away from the wall. So what height does it's top reach?

Let A be the foot of the ladder. B be the top of the ladder. C be the junction/corner of the wall and floor. AB = 6m, BC = 8 m... When AB = 8m.. Then BC becomes 6m., The sides AB and BC are interchanged, as the length AC is constant.

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The 'ladder', 'height to which it reaches' and 'foot of ladder from wall' forms a right angled triangle. ladder = hypotenuse(h) height to which it reaches = base(b) foot of ladder from wall = altitude(a)

initially, a = 8m, b = 6m h² = a² + b² ⇒ h = √(a²+b²) = √(8² + 6²) = √100 = 10m

when foot is 8m away from wall, b = 8m, h = 10m, a = ? h² = a² + b² ⇒ a² = h² - b² ⇒ a = √(h² - b²) = √(10² - 8²) = √36 = 6m

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6 Metres

6m sq + 8 m sq=x m sq 100 m = x m sq x= 10 m= length of ladder

base= 8 m length of ladder= 10 m therefore height from ground to top = uder root of( 10 m sq - 8 m sq)= 6METRES