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15. In the adjoining given figure, AABC is a right triangle, right angled atO B. AD and CE are two medians drawn from A and C respectivelyA0If AC 5 cm andD 375 cm, then find the length of CE.th2 |
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Answer» We apply Pythagoras theorem.ΔABC: AC² = AB² + BC² 5² = (2 BE)² + BC² 25 = 4BE² + BC² -- (1)Also, BE² + BC² = CE² ----(2)ΔABD, AD² = AB² + BD² = 4 BE² + BC²/4=> 4 (3√5/2)² = 45 =16 BE² + BC² -- (3)Solve the equations (1) and (2). 55 = 3 BC² => BC =√(55/3)=> BE² = (AC² - BC²)/4 =(5² - 55/3)/4 = 5/3 By (2), CE² = 5/3 + 55/3 = 20/3=> CE = 2√(5/3) |
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