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The height of a triangle is increased by 40%. what can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 60% ?
Please elaborate me how you deduced yourself to the conclusion?
Please elaborate me how you deduced yourself to the conclusion?
Verified Answer
The height of a triangle is increased by 40%. what can be the maximum ...
Let the height be h and base be b.
Height increases 40%,So new height = h + 40% of h = 7/5*h
Area of triangle = (� * h * b)
Area increases by 60%. so, new area,
= (� * h * b) + 60% of (� * h * b)
= 8/5*1/2*b*h
Let new base be x, then
New area,= 1/2*7/5*x = 8/5*1/2*b*h
which will result into x = 8/7*b
So, base will increase by 1/7th of b = 14.28%.
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The height of a triangle is increased by 40%. what can be the maximum ...
Solution:
Given:
- The height of a triangle is increased by 40%.
- The maximum increase in length of the base is to be found so that the increase in area is restricted to a maximum of 60%.
To solve this problem, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
Let the original height of the triangle be h and the original base be b.
New height = 1.4h (40% increase in height)
New area = 1/2 * b * 1.4h = 0.7bh
We want the increase in area to be restricted to a maximum of 60%.
Therefore,
0.7bh - bh ≤ 0.6bh
0.1bh ≤ 0.7bh
0.6bh ≤ 0
This is not possible, so there is no maximum percentage increase in length of the base that can restrict the increase in area to a maximum of 60%.
Explanation:
- We begin by using the formula for the area of a triangle, which is given as 1/2 * base * height.
- We are given that the height of the triangle is increased by 40%, which means that the new height is 1.4 times the original height.
- We can then use this information to find the new area of the triangle, which is 1/2 * base * 1.4h.
- We want the increase in area to be restricted to a maximum of 60%, which means that the new area can be at most 1.6 times the original area.
- We set up an inequality to represent this condition and then simplify it.
- We find that the inequality is not possible, which means that there is no maximum percentage increase in length of the base that can restrict the increase in area to a maximum of 60%.
Therefore, the answer is that there is no maximum percentage increase in length of the base that can restrict the increase in area to a maximum of 60%.
Given:
- The height of a triangle is increased by 40%.
- The maximum increase in length of the base is to be found so that the increase in area is restricted to a maximum of 60%.
To solve this problem, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
Let the original height of the triangle be h and the original base be b.
New height = 1.4h (40% increase in height)
New area = 1/2 * b * 1.4h = 0.7bh
We want the increase in area to be restricted to a maximum of 60%.
Therefore,
0.7bh - bh ≤ 0.6bh
0.1bh ≤ 0.7bh
0.6bh ≤ 0
This is not possible, so there is no maximum percentage increase in length of the base that can restrict the increase in area to a maximum of 60%.
Explanation:
- We begin by using the formula for the area of a triangle, which is given as 1/2 * base * height.
- We are given that the height of the triangle is increased by 40%, which means that the new height is 1.4 times the original height.
- We can then use this information to find the new area of the triangle, which is 1/2 * base * 1.4h.
- We want the increase in area to be restricted to a maximum of 60%, which means that the new area can be at most 1.6 times the original area.
- We set up an inequality to represent this condition and then simplify it.
- We find that the inequality is not possible, which means that there is no maximum percentage increase in length of the base that can restrict the increase in area to a maximum of 60%.
Therefore, the answer is that there is no maximum percentage increase in length of the base that can restrict the increase in area to a maximum of 60%.
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The height of a triangle is increased by 40%. what can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 60% ?Please elaborate me how you deduced yourself to the conclusion?
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The height of a triangle is increased by 40%. what can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 60% ?Please elaborate me how you deduced yourself to the conclusion? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The height of a triangle is increased by 40%. what can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 60% ?Please elaborate me how you deduced yourself to the conclusion? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The height of a triangle is increased by 40%. what can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 60% ?Please elaborate me how you deduced yourself to the conclusion?.
The height of a triangle is increased by 40%. what can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 60% ?Please elaborate me how you deduced yourself to the conclusion? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The height of a triangle is increased by 40%. what can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 60% ?Please elaborate me how you deduced yourself to the conclusion? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The height of a triangle is increased by 40%. what can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 60% ?Please elaborate me how you deduced yourself to the conclusion?.
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