Question : The sides of a triangle are in the ratio 7 : 9 : 12. The difference between the lengths of the largest and smallest sides is 15 cm. The length of the largest side would be (in cm):
Option 1: 36
Option 2: 12
Option 3: 60
Option 4: 24
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Correct Answer: 36
Solution :
Given: The sides of a triangle are in the ratio of 7 : 9 : 12.
Let the sides of the triangle be $7x, 9x$, and $12x$.
According to the question,
$12x -7x = 15$
⇒ $5x = 15$
⇒ $x = \frac{15}{5} = 3$
Largest side $=12x = 12 × 3= 36$ cm
Hence, the correct answer is 36.
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