Question

Mr. a has, 34 feet of edging to enclose a rectangular prism. What veggies and width would make the garden with the greatest area? Find the greatest area.

Answer 1

Let the length be represented by "l" and the width be represented by "w".

The perimeter of the rectangular prism is given as:
Perimeter = 2(l + w) = 34
l + w = 17

We want to maximize the area of the rectangular prism, which is given by:
Area = l * w

From the equation l + w = 17, we can express l in terms of w:
l = 17 - w

Substitute this into the area equation:
Area = (17 - w) * w
Area = 17w - w^2

To find the value of w that maximizes the area, we take the derivative of the area equation with respect to w and set it equal to 0:
d(Area)/dw = 17 - 2w
17 - 2w = 0
2w = 17
w = 8.5

Since the width cannot be a decimal number, we round it down to the nearest whole number, which is 8. This means the width should be 8 feet.

To find the length, we use the equation l + w = 17:
l + 8 = 17
l = 9

Therefore, the length should be 9 feet.

To find the greatest area, we substitute the length and width back into the area equation:
Area = 9 * 8
Area = 72 square feet

So, the greatest area of the rectangular prism would be 72 square feet with a length of 9 feet and a width of 8 feet.