A tree of height 36m is on one edge of a road broke at a certain height. It…
2024
A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke?
- A.
16
- B.
24
- C.
12
- D.
18
Attempted by 2 students.
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Correct answer: A
Let the height at which the tree broke be h meters. The remaining part of the tree that fell is (36 - h) meters.
This fallen part forms the hypotenuse of a right triangle, where the base is the width of the road (12m) and the height is h.
Using Pythagoras' theorem: (36 - h)^2 = h^2 + 12^2.
Expand and simplify: 1296 - 72h + h^2 = h^2 + 144.
Subtract h^2 from both sides: 1296 - 72h = 144.
Solve for h: 72h = 1152 → h = 16.