Question

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,

Answer 1

length = 12.5 in, width = 12.5 in, Area = 156.25 in²

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:

• 2x + 2x = 50
• 4x = 50
• x = 12.5

The area of the rectangle is calculated using the formula:

• A = lw

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

• A = x²

Substitute x = 12.5 into this equation.

• A = (12.5)²
• A = 156.25

The maximum area that can be formed from the wire is 156.25 in², and the dimensions of the rectangle are 12.5 x 12.5 in.