Question

Find the dimensions of the rectangle of maximum area that can be formed from a 50-m piece of wire. (Use decimal notation. Give your answer to two decimal places, if necessary.)

A) Maximum area: m², Length of the rectangle: m, Width of the rectangle: m
B) Maximum area: cm², Length of the rectangle: cm, Width of the rectangle: cm
C) Maximum area: ft², Length of the rectangle: ft, Width of the rectangle: ft
D) Maximum area: km², Length of the rectangle: km, Width of the rectangle: km

Answer 1

To find the dimensions of the rectangle of maximum area, we can use the formula for the perimeter of a square and set it equal to the given wire length. Solving for the side length, we find that the maximum area is 156.25 square meters.

Step-by-step explanation:

To find the dimensions of the rectangle of maximum area that can be formed from a 50-m piece of wire, we need to understand that the maximum area of a rectangle is achieved when it is a square. Since the wire length is 50 meters, we can use a formula to calculate the side length of the square. Let's call the side length 'x'.

Perimeter of the square = 4x

Since the wire length is 50 meters, we can set up the equation: 4x = 50

Solving for x, we have x = 50 / 4 = 12.5 meters.

Therefore, the maximum area of the rectangle is 12.5 meters by 12.5 meters, or 156.25 square meters.