Q2 of 99 Page 258

In a lake of Botanical Garden the tip of lotus was seen 2 cm. above the surface of water. Being forced by the wind, it gradually advanced and submerged at a distance of 15 cm. from the previous position. Let us write by calculating the depth of water.


Let the depth of the water be BD = x cm


According to the given condition


AD = CD = (x + 2) cm because the straight lotus submerged into lake covering distance BC = 15cm


Now in right angled triangle DBC


CD = x + 2, is hypotenuse


BC = 15, is base and


BD = x, is the height which is also the depth of water


According to the Pythagoras theorem


Hypothenuse2 = Base2 + height2


CD2 = BD2 + BC2


(x + 2)2 = x2 + 152


⇒ x2 + 4 + 4x = x2 + 225 (∵ (a + b)2 = a2 + b2 + 2ab)


⇒ 4x = 221


⇒


⇒ x = 55.25 cm


The depth of water = 55.25cm


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