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 x. (2022)

Options:

Correct Answer: 50

Exam Year: 2022

Solution:

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

Find the maximum area of a triangle with a base of 10 units and height as a function of x. (2022)

Find the maximum area of a triangle with a base of 10 units and height as a function of x. (2022)

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: Recognize that the height can change, but we want to find the maximum area.
Step 4: To find the maximum area, we need to maximize the height. The maximum height is given as 10 units.
Step 5: Substitute the base and maximum height into the area formula: Area = 1/2 * 10 * 10.
Step 6: Calculate the area: Area = 1/2 * 10 * 10 = 50 square units.
Step 7: Conclude that the maximum area of the triangle is 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 maximize the height while keeping the base constant.