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If the length of each side of a triangle is multiplied by 3, then the % increase in area will be:
- a)400%
- b)800%
- c)700%
- d)900%
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the length of each side of a triangle is multiplied by 3, then the ...
Understanding Area of a Triangle
The area of a triangle is given by the formula:
Area = 1/2 * base * height.
When the lengths of the sides of a triangle are multiplied by a factor, the area changes based on the square of that factor.
Effect of Scaling on Area
- If each side of the triangle is multiplied by 3, the new lengths become 3 times the original lengths.
- The new area can be calculated as:
New Area = 1/2 * (3 * base) * (3 * height) = 9 * (1/2 * base * height) = 9 * Original Area.
Calculating the Percentage Increase
- The increase in area can be determined as follows:
Increase in Area = New Area - Original Area = 9 * Original Area - Original Area = 8 * Original Area.
- To find the percentage increase, we use the formula:
Percentage Increase = (Increase in Area / Original Area) * 100.
- Substituting the values, we get:
Percentage Increase = (8 * Original Area / Original Area) * 100 = 800%.
Final Conclusion
Thus, when the length of each side of a triangle is multiplied by 3, the area increases by 800%. Therefore, the correct answer is option 'B'.
The area of a triangle is given by the formula:
Area = 1/2 * base * height.
When the lengths of the sides of a triangle are multiplied by a factor, the area changes based on the square of that factor.
Effect of Scaling on Area
- If each side of the triangle is multiplied by 3, the new lengths become 3 times the original lengths.
- The new area can be calculated as:
New Area = 1/2 * (3 * base) * (3 * height) = 9 * (1/2 * base * height) = 9 * Original Area.
Calculating the Percentage Increase
- The increase in area can be determined as follows:
Increase in Area = New Area - Original Area = 9 * Original Area - Original Area = 8 * Original Area.
- To find the percentage increase, we use the formula:
Percentage Increase = (Increase in Area / Original Area) * 100.
- Substituting the values, we get:
Percentage Increase = (8 * Original Area / Original Area) * 100 = 800%.
Final Conclusion
Thus, when the length of each side of a triangle is multiplied by 3, the area increases by 800%. Therefore, the correct answer is option 'B'.
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Community Answer
If the length of each side of a triangle is multiplied by 3, then the ...
Let the sides be a, b, c.
∴ New sides = 3a, 3b, 3c.
∴ snew = 3s.
New area =
= 9∆
∴ Increase in area = 9∆ – ∆ = 8∆
∴ % Increase in area =
∴ New sides = 3a, 3b, 3c.
∴ snew = 3s.
New area =
= 9∆
∴ Increase in area = 9∆ – ∆ = 8∆
∴ % Increase in area =
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If the length of each side of a triangle is multiplied by 3, then the % increase in area will be:a)400%b)800%c)700%d)900%Correct answer is option 'B'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If the length of each side of a triangle is multiplied by 3, then the % increase in area will be:a)400%b)800%c)700%d)900%Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the length of each side of a triangle is multiplied by 3, then the % increase in area will be:a)400%b)800%c)700%d)900%Correct answer is option 'B'. Can you explain this answer?.
If the length of each side of a triangle is multiplied by 3, then the % increase in area will be:a)400%b)800%c)700%d)900%Correct answer is option 'B'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If the length of each side of a triangle is multiplied by 3, then the % increase in area will be:a)400%b)800%c)700%d)900%Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the length of each side of a triangle is multiplied by 3, then the % increase in area will be:a)400%b)800%c)700%d)900%Correct answer is option 'B'. Can you explain this answer?.
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