Question

One side of a rectangle is 12 m longer than four times another side. Find the length of the sides, given that the area of the rectangle is 216 m². What is the length of the sides?"

Answer 1

To find the lengths of the sides of the rectangle, set up the equation x(4x + 12) = 216 based on the given area and relationship between sides. Solving this gives a quadratic equation, and the lengths are found to be 6 meters and 36 meters.

Step-by-step explanation:

To solve the problem of finding the lengths of the sides of the rectangle, we need to set up two equations based on the information given:

• Let x represent the length of one side of the rectangle.
• Then, the length of the other side is 4x + 12 meters.
• The area of the rectangle is given as 216 m², so we can write the equation x(4x + 12) = 216.

Expanding this equation gives us a quadratic equation:

• 4x² + 12x - 216 = 0.

To solve for x, we can factor the quadratic or use the quadratic formula. Factoring the equation, we find that (x - 6)(4x + 36) = 0, which gives us potential solutions for x as x = 6 or x = -9. Since a negative length does not make sense in this context, we take x = 6. This means one side of the rectangle is 6 meters, and the other side is 4(6) + 12 = 36 meters.

The lengths of the sides of the rectangle are therefore 6 meters and 36 meters.