Question

The perimeter of a rectangular piece of property is 8 miles and it's area is 3 square miles, find the dimensions

Answer 1

Let's assume the length of the rectangular property is L miles and the width is W miles.

The perimeter of the rectangular property is given by the formula:

Perimeter = 2(L + W)

Since the perimeter is given as 8 miles, we can write the equation:

2(L + W) = 8

Simplifying this equation, we have:

L + W = 4

The area of the rectangular property is given by the formula:

Area = L * W

Since the area is given as 3 square miles, we can write the equation:

L * W = 3

Now, we have two equations:

Equation 1: L + W = 4
Equation 2: L * W = 3

We can solve these equations simultaneously to find the dimensions of the rectangular property.

From Equation 1, we can write:

L = 4 - W

Substituting this value of L in Equation 2, we have:

(4 - W) * W = 3

Expanding the equation, we get:

4W - W^2 = 3

Rearranging the equation, we have:

W^2 - 4W + 3 = 0

Factoring the quadratic equation, we have:

(W - 3)(W - 1) = 0

This gives us two possible values for W:

W = 3 or W = 1

If W = 3, then L = 4 - 3 = 1
If W = 1, then L = 4 - 1 = 3

Therefore, the dimensions of the rectangular property can be either 1 mile by 3 miles or 3 miles by 1 mile.