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)
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Step-by-Step Solution
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 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 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, c2=h2+b2, to find the length of the broken part (c). Substituting the given values, h=15 m and b=20 m, we calculate c to be 25 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 m and 25 m gives a total height of 40 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 m, 20 m, and 25 m gives a perimeter of 60 m.
Step 5: Calculate the area of the triangle
The area of a right-angled triangle is calculated using the formula 21×base×height. Substituting the base b=20 m and height h=15 m, we find the area to be 150 m2.