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A tree broke due to storm at a point but did not separate. Its top touch the ground at a distance of 10 meters from the base. The height of the point from the ground at which the was broken is 12/25 metre of the total height of the tree. Find the height of the tree.?
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A tree broke due to storm at a point but did not separate. Its top tou...
To solve the problem of the broken tree, we will break down the information provided and use basic geometry.
Understanding the Problem
- A tree broke at a certain height but remained attached.
- The top of the tree touches the ground 10 meters away from the base.
- The height at which the tree broke is \(\frac{12}{25}\) of the total height of the tree.
Let’s Define Variables
- Let the total height of the tree be \(H\) meters.
- The height at which the tree broke is given by \(\frac{12}{25}H\).
- The remaining height of the tree after it broke is \(H - \frac{12}{25}H = \frac{13}{25}H\).
Forming a Right Triangle
- When the top of the tree touches the ground, we can visualize a right triangle:
- One leg is the horizontal distance from the base to the point where the top touches the ground (10 meters).
- The other leg is the height of the remaining part of the tree (\(\frac{13}{25}H\)).
- The hypotenuse is the length of the tree from the break point to the top.
Applying the Pythagorean Theorem
- According to the Pythagorean theorem:
\[
\left(\frac{13}{25}H\right)^2 + 10^2 = \left(\frac{12}{25}H\right)^2
\]
- Simplifying this gives:
\[
\frac{169}{625}H^2 + 100 = \frac{144}{625}H^2
\]
Rearranging leads to:
\[
25 = \frac{144}{625}H^2 - \frac{169}{625}H^2
\]
\[
25 = -\frac{25}{625}H^2
\]
\[
H^2 = 625 \implies H = 25
\]
Conclusion
- Thus, the total height of the tree is **25 meters**.
Understanding the Problem
- A tree broke at a certain height but remained attached.
- The top of the tree touches the ground 10 meters away from the base.
- The height at which the tree broke is \(\frac{12}{25}\) of the total height of the tree.
Let’s Define Variables
- Let the total height of the tree be \(H\) meters.
- The height at which the tree broke is given by \(\frac{12}{25}H\).
- The remaining height of the tree after it broke is \(H - \frac{12}{25}H = \frac{13}{25}H\).
Forming a Right Triangle
- When the top of the tree touches the ground, we can visualize a right triangle:
- One leg is the horizontal distance from the base to the point where the top touches the ground (10 meters).
- The other leg is the height of the remaining part of the tree (\(\frac{13}{25}H\)).
- The hypotenuse is the length of the tree from the break point to the top.
Applying the Pythagorean Theorem
- According to the Pythagorean theorem:
\[
\left(\frac{13}{25}H\right)^2 + 10^2 = \left(\frac{12}{25}H\right)^2
\]
- Simplifying this gives:
\[
\frac{169}{625}H^2 + 100 = \frac{144}{625}H^2
\]
Rearranging leads to:
\[
25 = \frac{144}{625}H^2 - \frac{169}{625}H^2
\]
\[
25 = -\frac{25}{625}H^2
\]
\[
H^2 = 625 \implies H = 25
\]
Conclusion
- Thus, the total height of the tree is **25 meters**.
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A tree broke due to storm at a point but did not separate. Its top touch the ground at a distance of 10 meters from the base. The height of the point from the ground at which the was broken is 12/25 metre of the total height of the tree. Find the height of the tree.?
Question Description
A tree broke due to storm at a point but did not separate. Its top touch the ground at a distance of 10 meters from the base. The height of the point from the ground at which the was broken is 12/25 metre of the total height of the tree. Find the height of the tree.? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A tree broke due to storm at a point but did not separate. Its top touch the ground at a distance of 10 meters from the base. The height of the point from the ground at which the was broken is 12/25 metre of the total height of the tree. Find the height of the tree.? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tree broke due to storm at a point but did not separate. Its top touch the ground at a distance of 10 meters from the base. The height of the point from the ground at which the was broken is 12/25 metre of the total height of the tree. Find the height of the tree.?.
A tree broke due to storm at a point but did not separate. Its top touch the ground at a distance of 10 meters from the base. The height of the point from the ground at which the was broken is 12/25 metre of the total height of the tree. Find the height of the tree.? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A tree broke due to storm at a point but did not separate. Its top touch the ground at a distance of 10 meters from the base. The height of the point from the ground at which the was broken is 12/25 metre of the total height of the tree. Find the height of the tree.? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tree broke due to storm at a point but did not separate. Its top touch the ground at a distance of 10 meters from the base. The height of the point from the ground at which the was broken is 12/25 metre of the total height of the tree. Find the height of the tree.?.
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A tree broke due to storm at a point but did not separate. Its top touch the ground at a distance of 10 meters from the base. The height of the point from the ground at which the was broken is 12/25 metre of the total height of the tree. Find the height of the tree.?, a detailed solution for A tree broke due to storm at a point but did not separate. Its top touch the ground at a distance of 10 meters from the base. The height of the point from the ground at which the was broken is 12/25 metre of the total height of the tree. Find the height of the tree.? has been provided alongside types of A tree broke due to storm at a point but did not separate. Its top touch the ground at a distance of 10 meters from the base. The height of the point from the ground at which the was broken is 12/25 metre of the total height of the tree. Find the height of the tree.? theory, EduRev gives you an
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