Question : Asha and Suman's mud forts have heights of 9 cm and 16 cm. They are 24 cm apart. How far (in cm) are the fort tops from each other?
Option 1: 25
Option 2: 24
Option 3: 7
Option 4: 16
Correct Answer: 25
Solution : Height of Asha's mud fort = AB = 9 cm Height of Suman's mud fort = DE = 16 cm Distance between mud forts = BD = 24 cm AB = CD AC = BD From the above figure, DE = CD + CE ⇒ DE = AB + CE ⇒ CE = DE – AB ⇒ CE = 16 – 9 ⇒ CE = 7 cm In ΔACE, By using Pythagoras theorem, $(\text{AE})^2 = (\text{AC})^2 + (\text{CE})^2$ ⇒ $(\text{AE})^2$ = (24) 2 + (7) 2 ⇒ $(\text{AE})^2$ = 576 + 49 ⇒ $(\text{AE})^2$ = 625 ⇒ AE = $\sqrt{625} $ ⇒ AE = 25 cm $\therefore$ The fort tops are 25 cm far from each other. Hence, the correct answer is 25 cm.
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