Question : BE and CF are two altitudes of a triangle ABC. If AB = 6 cm, AC = 5 cm, and CF = 4 cm. Then, the length of BE is:
Option 1: 4.8 cm
Option 2: 7.5 cm
Option 3: 3.33 cm
Option 4: 5.5 cm
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Correct Answer: 4.8 cm
Solution :
Given: BE and CF are two altitudes of a triangle ABC.
Where AB = 6 cm, AC = 5 cm and CF = 4 cm
Area of $\triangle ABC = \frac{1}{2}\times AB\times CF= \frac{1}{2}\times AC\times BE$
$⇒\frac{1}{2}\times 6\times 4= \frac{1}{2}\times 5\times BE$
$⇒BE = \frac{24}{5}=4.8$ cm
Hence, the correct answer is 4.8 cm.
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