Sukesh is having a garden at the back of his house with trees and flower plants. One day, due to heavy rain and storm, one of the trees broke such that the height of unbroken part is 15 m and the broken part of the tree bends and touches the ground at 20 m away from the base of the tree. Based on the above information, answer the following questions : (i) Find the length of the broken part of the tree. (1) (ii) What was the height of the full tree ? (1) (iii) (a) Find the perimeter of the triangle formed. (2) OR (b) Find the area of the triangle formed. (2)

Step 1: Identify the right-angled triangle

The problem describes a situation that forms a right-angled triangle. The unbroken part of the tree forms the height ($h$) of the triangle, which is $15\text{ m}$. The distance from the base of the tree to where the broken part touches the ground forms the base ($b$) of the triangle, which is $20\text{ m}$. The broken part of the tree forms the hypotenuse ($c$) of this right-angled triangle.

Step 2: Calculate the length of the broken part (hypotenuse)

We can use the Pythagorean theorem, $c^2 = h^2 + b^2$, to find the length of the broken part ($c$). Substituting the given values, $h = 15\text{ m}$ and $b = 20\text{ m}$, we calculate $c$ to be $25\text{ m}$.

Step 3: Calculate the total height of the tree

The total height of the tree before it broke is the sum of the unbroken part ($h$) and the broken part ($c$). Adding $15\text{ m}$ and $25\text{ m}$ gives a total height of $40\text{ m}$.

Step 4: Calculate the perimeter of the triangle

The perimeter of the right-angled triangle formed by the tree parts and the ground is the sum of its three sides: the height ($h$), the base ($b$), and the hypotenuse ($c$). Adding $15\text{ m}$, $20\text{ m}$, and $25\text{ m}$ gives a perimeter of $60\text{ m}$.

Step 5: Calculate the area of the triangle

The area of a right-angled triangle is calculated using the formula $\frac{1}{2} \times \text{base} \times \text{height}$. Substituting the base $b = 20\text{ m}$ and height $h = 15\text{ m}$, we find the area to be $150\text{ m}^2$.

More from this chapter

• In a right triangle the two legs are 3 cm and 4 cm. Find the hypotenuse and sin of the angle opposite the 3 cm side.
• It's a right angle triangle and you know one of the sides is 5 cm the other is 3 cm what is the third side
• Solve the Diophantine equation x² + y² = z² in positive integers (Pythagorean triples).

All The Baudhayana-Pythagoras Theorem solutions →