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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