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

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Question: Determine 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 is maximized, thus Area = 50 when h = 10.

Determine the maximum area of a triangle with a base of 10 units and height as a function of x. (2020)

Determine 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 maximize the height (h).
Step 6: The maximum height is given as 10 units (the maximum height the triangle can have).
Step 7: Substitute the maximum height back into the area formula: Area = 5 * 10.
Step 8: Calculate the maximum 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 – To find the maximum area, one must identify the maximum value of the height given the constraints.