164k views
2 votes
f the perimeter of the window is 16 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted.

User Nils Lande
by
5.7k points

1 Answer

1 vote

Final answer:

To maximize the amount of light admitted through a window, we need to maximize the window area. The maximum area occurs when the width and length of the window are both 4 feet.

Step-by-step explanation:

To maximize the amount of light admitted through a window, we need to maximize the window area. Let's assume the window is rectangular with width x and length y.

The perimeter of the window is given as 16 feet, so we can write the equation 2x + 2y = 16.

To find the maximum area, we can solve for y in terms of x, substitute it back into the area formula, and then take the derivative with respect to x to find the value of x that maximizes the area. The maximum area occurs when x = y = 4 feet.

User Datchung
by
5.5k points