Question : The sides of a triangle are in the ratio $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ and its perimeter is 104 cm. The length of the longest side (in cm) is:
Option 1: 52
Option 2: 48
Option 3: 32
Option 4: 26
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Correct Answer: 48
Solution :
Given: The ratio of the triangle's sides
$=\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$.
$=\frac{1}{2} × 12 : \frac{1}{3} × 12 : \frac{1}{4} × 12$
$=6: 4: 3$
The perimeter of the triangle is $104$ cm.
$\therefore$ The longest length of the triangle = $\frac{104}{6+4+3}×6= 48$ cm
Hence, the correct answer is 48.
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