The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is
a. 25 m
b. 13 m
c. 18 m
d. 17 m
Solution:
Given, the top of a broken tree touches the ground at a distance of 12 m from its base.
The tree is broken at a height of 5 m from the ground.
We have to find the actual height of the tree.
Let AB be the height of the tree.
AB = h m
BC be the height from the ground where the tree is broken
BC = 5 m
BD is the distance from the base and top of the tree where it touches the ground
BD = 12 m
We know that AC = CD, length of the broken tree.
AB = AC + BC
h = AC + 5
AC = h - 5
So, CD = h - 5
By using pythagorean theorem,
CD² = AB² + BD²
(h - 5)² = 5² + 12²
(h - 5)² = 25 + 144
(h - 5)² = 169
Taking square root,
h - 5 = 13
h = 13 + 5
h = 18 m
Therefore, the height of the tree is 18 m.
✦ Try This: The top of a broken tree touches the ground at a distance of 14 m from its base. If the tree is broken at a height of 6 m from the ground then the actual height of the tree is
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 11
The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is: a. 25 m, b. 13 m, c. 18 m, d. 17 m
Summary:
The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is 18 m
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