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If we increase the length of the base of a triangle to four times, by how many times its area will increase?
- a)Two times
- b)Four times
- c)Eight times
- d)Sixteen times
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If we increase the length of the base of a triangle to four times, by ...
Explanation:
When the length of the base of a triangle is increased by a certain factor, the area of the triangle will also increase by the square of that factor.
In this case, the length of the base is increased by four times. Let's assume the original length of the base is 'b'.
So, the new length of the base will be 4b.
Formula for calculating the area of a triangle:
Area = (1/2) * base * height
The base of the triangle is increased by 4 times, but the height remains the same. Let's assume the height is 'h'.
Now we can calculate the original area of the triangle using the formula:
Original Area = (1/2) * b * h
And the new area of the triangle with the increased base:
New Area = (1/2) * (4b) * h = 2 * b * h
Calculating the ratio of the new area to the original area:
Ratio = New Area / Original Area = (2 * b * h) / ((1/2) * b * h)
Simplifying the equation, we get:
Ratio = 2 * b * h * 2 / b * h
The height 'h' cancels out, and the ratio simplifies to:
Ratio = 4
Therefore, the area of the triangle will increase by four times when the length of the base is increased by four times.
Hence, the correct answer is option 'B' - Four times.
When the length of the base of a triangle is increased by a certain factor, the area of the triangle will also increase by the square of that factor.
In this case, the length of the base is increased by four times. Let's assume the original length of the base is 'b'.
So, the new length of the base will be 4b.
Formula for calculating the area of a triangle:
Area = (1/2) * base * height
The base of the triangle is increased by 4 times, but the height remains the same. Let's assume the height is 'h'.
Now we can calculate the original area of the triangle using the formula:
Original Area = (1/2) * b * h
And the new area of the triangle with the increased base:
New Area = (1/2) * (4b) * h = 2 * b * h
Calculating the ratio of the new area to the original area:
Ratio = New Area / Original Area = (2 * b * h) / ((1/2) * b * h)
Simplifying the equation, we get:
Ratio = 2 * b * h * 2 / b * h
The height 'h' cancels out, and the ratio simplifies to:
Ratio = 4
Therefore, the area of the triangle will increase by four times when the length of the base is increased by four times.
Hence, the correct answer is option 'B' - Four times.
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If we increase the length of the base of a triangle to four times, by how many times its area will increase?a)Two timesb)Four timesc)Eight timesd)Sixteen timese)None of theseCorrect answer is option 'B'. Can you explain this answer?
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