The area of a rectangular park is 4 mi^2. The park has a width that is equal to "w", and a length that is 3 mi longer than the width of the park. Find the dimensions of the park.

l = 4 mi : width of the park

w = 1 mi : length of the park

Explanation:

Formula to find the area of the rectangle:

A = w*l Formula (1)

Where,

A is the area of the rectangle in mi²

w is the width of the rectangle in mi

l is the width of the rectangle in mi

Known data

A = 4 mi²

l = (w+3) mi Equation (1)

Problem development

We replace the data in the formula (1)

A = w*l

4 = w * (w+3)

4 = w²+3w

w²+3w-4 = 0

We factor the equation:

We look for two numbers whose sum is 3 and whose multiplication is - 4

(w-1) (w+4) = 0 Equation (2)

The values of w for which the equation (2) is zero are:

w = 1 and w = - 4

We take the positive value w = 1 because w is a dimension and cannot be negative.

w = 1 mi : width of the park

We replace w = 1 mi in the equation (1) to calculate the length of the park:

l = (w+3) mi

l = (1+3) mi

l = 4 mi