1. Two poles of height 2 meters and 3 meters are 5 meters apart. The height of the point of intersection of the lines joining the top of each poles to the foot of the opposite pole is,
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Solution : In $$ riangle$$ ABC and $$ riangle$$ EFC $$angle ACB = angle ECF$$ (common) $$angle ABC = angle EFC = 90$$
=> $$ riangle ABC sim riangle EFC$$ => $$frac{x}{2} = frac{5 - d}{5}$$ ----------Eqn(I) Similarly, $$ riangle BCD sim riangle BFE$$ => $$frac{x}{3} = frac{d}{5}$$ --------Eqn(II) Adding Eqns (I) & (II), we get : => $$frac{x}{2} + frac{x}{3} = frac{5 - d}{5} + frac{d}{5}$$ => $$frac{3x + 2x}{6} = frac{5}{5}$$ => $$5x = 6 imes 1 = 6$$ => $$x = frac{6}{5} = 1.2 m$$