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Suresh is having a garden near Delhi. In the garden, there are different types of trees and flower plants. One day, due to heavy rain and storm one of the trees got broken as shown in the figure. The height of the unbroken part is 15 m and the broken part of the tree has fallen at 20 m away from the base of tree(i). What is the length of the broken part ?(a) 15 m(b) 20 m(c) 25 m(d) 30 m.(ii). What was the height of the full tree ?(a) 40 m(b) 50 m(c) 35 m(d) 30 m.(iii). In the formed right-angled triangle, what is the length of the hypotenuse ?(a) 15 m(b) 20 m(c) 25 m(d) 30 m.(iv). What is the area of the formed right angle triangle ?(a) 100 m2(b) 200 m2(c) 60 m2(d) 150 m2.(v). What is the perimeter of the formed triangle ?(a) 60 m(b) 45 m(c) 50 m(d) 100 m. |
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Answer» Let the length of the broken part of the tree is = x m. Given that the height of the unbroken part is AC = 15 m And the broken part of the tree has fallen at 20 m away from the base of tree. i.e., AB = 20 m. Therefore, the height of the unbroken tree is (x + 15)m. (i). In right angled triangle ∆ABC, BC2 = AB2 + AC2 (By Pythagoras theorem in ∆ABC, where angle \(\angle\)BAC is an right angle ) ⇒ x2 = 202 + 152 = 400 + 225 = 625 (By putting AB = 20 m, AC = 15 m and BC = x m) ⇒ x = \(\sqrt{625}\) = 25. Hence, the length of the broken part of the tree is 25 m. Hence, option (c) is correct. (ii). The height of the unbroken part of the tree is 15 m And the height of the broken part of the tree is 25 m. Therefore, the height of full tree is (15 + 25)m = 40 m. Hence, option (a) is correct. (iii). The length of the hypotenuse in the formed right angle triangle is BC = x = 25 m. Hence, option (c) is correct. (iv). We know that the area of a triangle is A = \(\frac{1}{2}\) × (Base) × (Height) square units. The height of right angle triangle ∆ABC is AC = 15 m. And the base of the right angle triangle is AB = 20 m. Therefore, the area of formed right angle triangle ∆ABC is \(\frac{1}{2}\) × AB × AC = \(\frac{1}{2}\) × 20 × 15 = 150 m2. Hence, option (d) is correct. (v). We know that the perimeter of a triangle is sum of the length of its sides. The sides of formed right angle triangle ∆ABC are AB = 20 m, AC = 15 m and BC = 25 m. Therefore, the perimeter of the formed triangle is AB + AC + BC = (20 + 15 + 25)m = 60 m. Hence, option (a) is correct. |
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