What is the maximum area of a triangle with a base of 10 units and height as a f

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Question: What is the maximum area of a triangle with a base of 10 units and height as a function of x? (2020)

Options:

Correct Answer: 50

Exam Year: 2020

Solution:

Area = 1/2 * base * height = 5h. Max area occurs when h = 10, giving area = 50.

What is the maximum area of a triangle with a base of 10 units and height as a function of x? (2020)

What is the maximum area of a triangle with a base of 10 units and height as a function of x? (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 units.
Step 3: Substitute the base into the area formula: Area = 1/2 * 10 * height.
Step 4: Simplify the equation: Area = 5 * height (or Area = 5h).
Step 5: To find the maximum area, we need to determine the maximum height (h).
Step 6: The problem states that the height can be a function of x, but we want the maximum height, which is 10 units.
Step 7: Substitute the maximum height into the area formula: Area = 5 * 10.
Step 8: Calculate the area: Area = 50 square units.

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