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If each side of an equilateral triangle is increased by 2 cm, then its area increases by 3√3 cm2. The length of its each side and its area are respectively equal to

  • a)
    3 cm, √3cm2

  • b)
    2 cm, √3cm2 

  • c)
    2 cm, √8 cm2

  • d)
    2 cm, √5 cm2

Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If each side of an equilateral triangle is increased by 2 cm, then its...
√3 cm².

Explanation:

Let's denote the original side length of the equilateral triangle as x.

Then, its original area would be:

A = (sqrt(3)/4) x²

Now, if we increase each side by 2 cm, the new side length would be x+2.

The new area can be calculated using the same formula:

A' = (sqrt(3)/4) (x+2)²

To find the increase in area, we can subtract the original area from the new area:

A' - A = (sqrt(3)/4) [(x+2)² - x²]

Expanding the brackets:

A' - A = (sqrt(3)/4) [x² + 4x + 4 - x²]

Simplifying:

A' - A = (sqrt(3)/4) (4x + 4)

A' - A = √3 (x+1)

We are given that this increase in area is equal to 3√3 cm²:

√3 (x+1) = 3√3

Solving for x:

x+1 = 3

x = 2

Therefore, the original side length of the equilateral triangle was 2 cm.

The new side length is x+2 = 4 cm.

The new area is:

A' = (sqrt(3)/4) (4)² = 4√3 cm²

And the increase in area was:

A' - A = 4√3 - (√3/4) (2)² = 3√3 cm²
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If each side of an equilateral triangle is increased by 2 cm, then its...
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If each side of an equilateral triangle is increased by 2 cm, then its area increases by 3√3cm2. The length of its each side and its area are respectively equal toa)3 cm,√3cm2b)2 cm, √3cm2c)2 cm,√8 cm2d)2 cm,√5 cm2Correct answer is option 'B'. Can you explain this answer?
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