A ladder 10 m long reaches a window which is 8 m above the ground on one side of the road,keeping its foot at the same point, the ladder is turned to the other side of the road to each a window 6 m high . what is the width of the road.
Answers
Given:
✰ A ladder 10 m long reaches a window which is 8 m above the ground on one side of the road.
✰ The foot of the ladder is kept at the same point.
✰ The ladder is turned to the other side of the road to each a window 6 m high.
To find:
✠ What is the width of the road.
Solution:
First we will assume that the width of the road be x. We will solve this problem by using Pythagoras theorem. We will find out the length of the base of both the ladders, then we will add them to find the breadth of the road because the foot of the ladder is kept at the same point.
Let's solve it...✧
Let the width of the road be x.
In ∆EFG, by using Pythagoras theorem,
➛ H² = P² + B²
Where,
- H = Hypotenuse of a right-angled triangle.
- P = Perpendicular of a right-angled triangle.
- B = Base of a right-angled triangle.
➛ EG² = EF² + FG²
➛ 10² = 8² + FG²
➛ 100 = 64 + FG²
➛ FG² = 100 - 64
➛ FG² = 36
➛ FG = √36
➛ FG = 6 m
then,
In ∆ABC, by using Pythagoras theorem,
➛ H² = P² + B²
Where,
- H = Hypotenuse of a right-angled triangle.
- P = Perpendicular of a right-angled triangle.
- B = Base of a right-angled triangle.
➛ AC² = AB² + BC²
➛ 10² = 6² + BC² [ Taking AC = 10 m ∵ the foot of the ladder is kept at the same point, so hypotenuse doesn't change ]
➛ 100 = 36 + BC²
➛ BC² = 100 - 36
➛ BC² = 64
➛ BC = √64
➛ BC = 8 cm
Now,
➤ The width of the road = FG + BC
➤ The width of the road = 6 + 8
➤ The width of the road = 14 m
∴ The width of the road = 14 m
_______________________________
Answer:
In ⊥ΔACB,∠C=90
∘
,BC=?
AC
2
+CB
2
=AB
2
(8)
2
+CB
2
=(10)
2
64+CB
2
=100
CB
2
=100−64
CB
2
=36
∴CB=6
∴ Ladder is at a distance of 6m from the base of the wall.
Explanation:
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