question_answer

Two poles of height 9 m and 14 m stand upright on a plane ground. If the distance between their tops in 13 m, find the distance between their feet.

Answer:

  In the above figure, AB and CD are two poles whose heights are 9 m and 14 m respectively. AB = EC = 9 m And      BD = 13 m DE = 14 - 9 = 5 m                                                                                                                           Now in right ABCDE, by Pythagoras  \[B{{D}^{2}}-\text{ }B{{E}^{2}}+\text{ }D{{E}^{2}}\] \[{{13}^{2}}-\text{ }B{{E}^{2}}-\text{ }{{5}^{2}}\]                                                                                                 \[B{{E}^{2}}\text{=}{{\left( 13 \right)}^{\text{2}}}\text{-}{{\left( 5 \right)}^{2}}\] = 169 - 25 \[B{{E}^{2}}-144\] \[BE=\sqrt{44}\] \[BE=12\text{ }m\], Hence, distance between their feet =12 m.