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Example 7 - A girl of height 90 cm is walking away from - Examples

  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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Example 7 A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds. Given: Lamp post (AB) = 3.6m Height of girl (CD)=90 cm = 90/100 m = 0.9 m Speed = 1.2 m/sec. To Find : Length of her shadow i.e. DE Solution: - The girl walks BD distance in 4 seconds We know that, Speed = π·π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’/(π‘‡π‘–π‘šπ‘’ ) Speed = π·π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’/(π‘‡π‘–π‘šπ‘’ ) 1.2 = 𝐡𝐷/4 1.2 Γ—4=𝐡𝐷 4.8 =𝐡𝐷 BD = 4.8 m Now , in βˆ† 𝐴𝐡𝐸 π‘Žπ‘›π‘‘ βˆ† 𝐢𝐷𝐸 ∠ E = ∠ E ∠ B = ∠ D Therefore, using AA Similarity criterion So, βˆ† 𝐴𝐡𝐸 ~ βˆ† 𝐢𝐷𝐸 We know that if two triangles are similar, their sides are in proportion 𝐡𝐸/𝐷𝐸=𝐴𝐡/𝐢𝐷 (𝐡𝐷 + 𝐷𝐸)/𝐷𝐸=𝐴𝐡/𝐢𝐷 (4.8 + 𝐷𝐸)/𝐷𝐸=3.6/0.9 (4.8 + 𝐷𝐸)/𝐷𝐸=36/9Γ—10/10 (4.8 + 𝐷𝐸)/𝐷𝐸=4 4.8 + DE = 4 Γ— DE 4.8 = 4DE – DE 4.8 = 3DE 3DE = 4.8 DE = 4.8/3 DE = 48/(3 Γ—10) DE = 16/10 = 1.6 m Hence , shadow is 1.6 m long

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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