Final answer:
To find the dimensions of the rectangle, set up a quadratic equation with the width as x and solve for x. The width is found to be 7 cm, and the length is x + 5 cm, which calculates to 12 cm. The dimensions are therefore 7 cm by 12 cm.
Step-by-step explanation:
To find the dimensions of a rectangle with an area of 84 cm² where the length is 5 cm more than the width, we can set up an equation. Let the width be x centimeters; then the length is x + 5 centimeters. We can express the area (A) as a function of width and length, A = length × width.
Therefore, the equation is x(x + 5) = 84. Let's solve this quadratic equation:
- x² + 5x - 84 = 0.
- Factoring the equation, we find: (x + 12)(x - 7) = 0.
- Setting each factor equal to zero gives us:
- x + 12 = 0 or x - 7 = 0.
- Thus, x = -12 (not a valid solution, as dimensions cannot be negative), or x = 7 cm, which is our width.
To find the length, we add 5 cm to our width: 7 cm + 5 cm = 12 cm.
The dimensions of the rectangle are 7 cm by 12 cm (Option B).