Question

Henry is planning to create two rectangular gardens. Henry uses the function g(n) = 5n² to determine the area, in square feet, of the second garden. The garden will be n feet wide. The garden will be created inside a square with side lengths of 100 feet. Each side of the garden will be parallel to a side of the square. Based on these constraints and the function g, what is the largest possible area that the second garden can have?

A. 2,000 square feet
B. 69,500 square feet
C. 10,000 square feet
D. 50,000 square feet

Answer 1

The largest possible area that the second garden can have is 500,000 square feet

Step-by-step explanation:

To find the largest possible area of the second garden, we need to find the maximum value of the function g(n) = 5n² within the given constraints. The garden will be created inside a square with side lengths of 100 feet, so the maximum width of the garden (n) is 100 feet. Plugging in n = 100 into the function, we get g(100) = 5(100)² = 500,000 square feet.

Therefore, the largest possible area that the second garden can have is 500,000 square feet.