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The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4. If the perimeter of the triangle is 52 cm, the length of the smallest side is
  • a)
    24 cm
  • b)
    18 cm
  • c)
    12 cm
  • d)
    9 cm
Correct answer is option 'C'. Can you explain this answer?
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The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4. If the perim...
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The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4. If the perim...
Given information:
- The sides of the triangle are in the ratio 1/2 : 1/3 : 1/4
- The perimeter of the triangle is 52 cm

Solution:

Step 1: Assign variables
Let the sides of the triangle be 1/2x, 1/3x, and 1/4x.

Step 2: Calculate the perimeter
The perimeter of the triangle is the sum of all three sides:
Perimeter = 1/2x + 1/3x + 1/4x = 52 cm
(6x + 4x + 3x) / 12 = 52
13x / 12 = 52
13x = 624
x = 48

Step 3: Calculate the length of the smallest side
The smallest side of the triangle is 1/4x:
1/4 * 48 = 12 cm
Therefore, the length of the smallest side of the triangle is 12 cm. Hence, option C is the correct answer.
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The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4. If the perimeter of the triangle is 52 cm, the length of the smallest side isa)24 cmb)18 cmc)12 cmd)9 cmCorrect answer is option 'C'. Can you explain this answer?
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