5. A 50-inch piece of wire is bent into the shape of a rectangle. Find the dimensions of the rectangle of maximum area that can be formed from the wire,

156.25 in²

Step-by-step explanation:

To get the maximum area, the wire can be shaped into a square. We can say that the length and width of the rectangle must be equal to each other, and call this value "x".

Therefore, we can write an equation for the perimeter:

The area of the rectangle is calculated using the formula:

Or in our case, the area of the rectangle is the area of a square:

Substitute x = 12.5 into this equation.

The maximum area that can be formed from the wire is 156.25 in².