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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