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The area of two equilateral triangle are in the ratio 196:169. What is the ratio between their perimeters?
  • a)
    13:14
  • b)
    14:13
  • c)
    1:14
  • d)
    14:1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The area of two equilateral triangle are in the ratio 196:169. What is...
Ratio of perimeters = ratio of sides 
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The area of two equilateral triangle are in the ratio 196:169. What is...
Understanding the Problem
The problem provides the areas of two equilateral triangles in the ratio 196:169 and asks for the ratio of their perimeters.
Area of an Equilateral Triangle
The area (A) of an equilateral triangle with side length 's' can be calculated using the formula:
- A = (√3/4) * s²
Area Ratio and Side Length Ratio
Given the area ratio:
- Area1 : Area2 = 196 : 169
If we denote the side lengths of the two triangles as s1 and s2, then:
- (√3/4) * s1² : (√3/4) * s2² = 196 : 169
This simplifies to:
- s1² : s2² = 196 : 169
Taking the square root of both sides gives:
- s1 : s2 = √196 : √169
- s1 : s2 = 14 : 13
Perimeter of an Equilateral Triangle
The perimeter (P) of an equilateral triangle is given by:
- P = 3 * s
Calculating the Perimeter Ratio
Therefore, the perimeter ratio is:
- P1 : P2 = 3 * s1 : 3 * s2
- Simplifying, we get: P1 : P2 = s1 : s2
Substituting the side length ratio:
- P1 : P2 = 14 : 13
Conclusion
Thus, the ratio of the perimeters of the two equilateral triangles is:
- 14:13
This confirms that the correct answer is option 'B'.
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