Question

One side of a rectangle is 12 mi longer than three times another side. Find the length of the sides, given that the area of the rectangle is 1440 mi2. Enter both sides, separated by a comma.

Answer 1

To find the length of the sides of the rectangle, use the formula for the area of a rectangle and solve the resulting quadratic equation. The length of the sides is 16 miles and 60 miles, respectively.

Step-by-step explanation:

To find the length of the sides of the rectangle, let's assume that one side is x miles. According to the problem, the other side is 12 miles longer than three times the first side. So, the second side can be represented as 3x + 12 miles.

The area of the rectangle is given as 1440 mi2. We can use the formula for the area of a rectangle, which is length multiplied by width. So, we have the equation:

x * (3x + 12) = 1440

Expand this equation:

3x2 + 12x = 1440

Now, let's solve the quadratic equation by setting it equal to zero:

3x2 + 12x - 1440 = 0

Factor the equation:

(3x - 48)(x + 30) = 0

Now, solve for x:

3x - 48 = 0, so x = 16

or

x + 30 = 0, so x = -30

Since the length of a side cannot be negative, we ignore the solution x = -30. Therefore, the length of the sides of the rectangle is 16 miles and 3(16) + 12 = 60 miles.