Find the maximum area of a triangle with a base of 10 units and height as a func

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Question: Find the maximum area of a triangle with a base of 10 units and height as a function of the base. (2021)

Options:

Correct Answer: 50

Exam Year: 2021

Solution:

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

Find the maximum area of a triangle with a base of 10 units and height as a function of the base. (2021)

Find the maximum area of a triangle with a base of 10 units and height as a function of the base. (2021)

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 units.
Step 3: Substitute the base into the area formula: Area = 1/2 * 10 * height.
Step 4: Simplify the formula: Area = 5 * height.
Step 5: To find the maximum area, we need to maximize the height. The maximum height is given as 10 units.
Step 6: Substitute the maximum height into the area formula: Area = 5 * 10.
Step 7: Calculate the area: Area = 50 square units.

Area of a Triangle – The area of a triangle is calculated using the formula Area = 1/2 * base * height.
Maximization – Understanding how to maximize the area by maximizing the height while keeping the base constant.