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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?
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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
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 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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