Question

6. The foot of a ladder is 6 m away from a wall and its top reaches a window 8 m above
the ground. If the ladder is shifted in such a way that its foot is 8 m away from the wall,
to what height does its top reach?
​

Answer 1

Answer:

case 1 -

Base =6m , perpendicular=8m, hypotenuse=?

h²=p²+b²

h²=8²+6²

h²=64+36

h²=100

h=10 m

case 2-

H=10m,p=? ,b=8m

h²=p²+b²

10²=p²+8²

100-64=p²

p²=36

p=√36

p=6m

height =6m

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• Distance btw. ladder and window = AC = 8cm
• Distance btw. foot of wall and window = CD = 6cm

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$\sf{\bold{\green{\underline{\underline{To\: Find}}}}}$

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• Height of wall ladder reaches when it is shifted at 8cm = BC = x = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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Triangle ACD is a right angled triangle.

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By using Pythagoras theorem;

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$\sf{\red{\boxed{\bold{h^2 = p^2 + b^2}}}}$

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(AD)² = (AC)² + (CD)²

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(AD)² = 8² + 6²

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(AD)² = 64 + 36

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(AD)² = 100

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AD = √100

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AD = 10cm

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Since the ladder is same ; therefore

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AD = BE = 10cm

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Now, in triangle BCE

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By using Pythagoras theorem;

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$\sf{\red{\boxed{\bold{h^2 = p^2 + b^2}}}}$

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(BE)² = (BC)² + (CE)²

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(10)² = (BC)² + (8)²

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100 = (BC)² + 64

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100 - 64 = (BC)²

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36 = (BC)²

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√36 = BC

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BC = 6cm

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• When the ladder is 8m away from the wall it will touch the wall at 6cm