Find the maximum area of a triangle with a base of 10 m and height varying. (202

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Question: Find the maximum area of a triangle with a base of 10 m and height varying. (2020)

Options:

Correct Answer: 50

Exam Year: 2020

Solution:

Area = 1/2 * base * height. Max area occurs when height is maximized, thus Area = 1/2 * 10 * 10 = 50.

Find the maximum area of a triangle with a base of 10 m and height varying. (2020)

Find the maximum area of a triangle with a base of 10 m and height varying. (2020)

Step 1: Understand the formula for the area of a triangle, which is Area = 1/2 * base * height.
Step 2: Identify the base of the triangle, which is given as 10 meters.
Step 3: Recognize that the height can vary, but to find the maximum area, we need to maximize the height.
Step 4: Assume the maximum height is also 10 meters (this is a common assumption for maximum area problems unless stated otherwise).
Step 5: Plug the values into the area formula: Area = 1/2 * 10 * 10.
Step 6: Calculate the area: Area = 1/2 * 100 = 50 square meters.
Step 7: Conclude that the maximum area of the triangle is 50 square meters.

Area of a Triangle – The area of a triangle is calculated using the formula Area = 1/2 * base * height, where the base and height are perpendicular to each other.
Maximizing Area – To find the maximum area, one must recognize that the area increases with height, thus the maximum area occurs at the maximum height.