Question : $\triangle DEF$ is right angled at E. EC is the altitude. CF is 18 cm and FD is 26 cm. What is the length of FE?
Option 1: $2\sqrt{13}$ cm
Option 2: $6\sqrt{13}$ cm
Option 3: $12$ cm
Option 4: $15$ cm
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Correct Answer: $6\sqrt{13}$ cm
Solution :
FD = 26 cm
CF = 18 cm
⇒ CD = 26 – 18 = 8 cm
EC
2
= CD × CF = 8 × 18 = 144
⇒ EC = $\sqrt {144}$ = 12 cm
In $\triangle$ECF, $\angle$ C = $90^{\circ}$
By Pythagoras theorem,
EF
2
= EC
2
+ CF
2
⇒ EF
2
= $12^2 + 18^2$
⇒ EF = $\sqrt{144+324}$
= $\sqrt{468}$
= $6\sqrt{13}$
Hence, the correct answer is $6\sqrt{13}$ cm.
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