What is the maximum area of a triangle with a base of 10 cm and height as a func

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

Options:

Correct Answer: 50

Exam Year: 2020

Solution:

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

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

What is the maximum area of a triangle with a base of 10 cm 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 cm.
Step 3: Let the height of the triangle be represented by 'x'.
Step 4: Substitute the base and height into the area formula: Area = 1/2 * 10 * x.
Step 5: Simplify the formula: Area = 5 * x.
Step 6: To find the maximum area, note that 'x' (the height) can be at most 10 cm, since the height cannot exceed the base in this context.
Step 7: Substitute x = 10 into the area formula: Area = 5 * 10.
Step 8: Calculate the area: Area = 50 cm².

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