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There are two buildings in two sides of a road. Keeping the foot of a ladder fixed at a point on the road, when it is placed on two buildings, then its top touches the buidings respectively at a height of 48 ft and 14 ft. If the length of the ladder is 50 ft, then the width of the road is :

  1. 56 ft

  2. 62 ft

  3. 66 ft

  4. 70 ft

Pythagoras Theorem

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Answer

There are two buildings in two sides of a road. Keeping the foot of a ladder fixed at a point on the road, when it is placed on two buildings, then its top touches the buidings respectively at a height of 48 ft and 14 ft. If the length of the ladder is 50 ft, then the width of the road is.Pythagoras Theorem, R.S. Aggarwal Mathematics Solutions ICSE Class 9.

Let width of the street be AB = AC + BC

Let CD and CE be the ladder at different positions.

By Pythagoras theorem,

Hypotenuse2 = Perpendicular2 + Base2

In triangle ADC,

⇒ CD2 = AD2 + AC2

⇒ 502 = 142 + AC2

⇒ 2500 = 196 + AC2

⇒ AC2 = 2500 - 196

⇒ AC2 = 2304

⇒ AC = 2304\sqrt{2304}

⇒ AC = 48 ft

In triangle BCE,

⇒ CE2 = BE2 + BC2

⇒ 502 = 482 + BC2

⇒ 2500 = 2304 + BC2

⇒ BC2 = 2500 - 2304

⇒ BC2 = 196

⇒ BC = 196\sqrt{196}

⇒ BC = 14 ft

AB = AC + BC = 48 + 14 = 62 ft.

Hence, option 2 is the correct option.

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