Question

A dog crate is built using 24 m^2 of wire. What is the biggest size possible for the dog crate?

a) 6 m by 4 m
b) 8 m by 3 m
c) 12 m by 2 m
d) 24 m by 1 m

Answer 1

The biggest size possible for the dog crate is option c) 12 m by 2 m.

Step-by-step explanation:

To find the biggest size possible for the dog crate, we need to determine the dimensions that will maximize the volume while using 24 m2 of wire. Let's consider option c) 12 m by 2 m as an example.

The perimeter of the crate is given by the sum of all sides. For option c), the perimeter is 2(12) + 2(2) = 28 m.

We know that the wire used to build the crate has an area of 24 m2 and the perimeter is 28 m. To find the width of the wire used, we can divide the area by the perimeter: 24 m2 / 28 m = 0.857 m.

Since the wire is used to make up the length and the width of the crate, we can divide the perimeter by 2 to get the dimensions: 12 m by 0.857 m.

Therefore, the biggest size possible for the dog crate is option c) 12 m by 2 m.