Final answer:
To find the dimensions of a rectangle with a given area, we need to set up and solve a quadratic equation.
Step-by-step explanation:
To find the dimensions of the rectangle, let's assign variables. Let's say the width of the rectangle is 'w' centimeters. According to the problem, the length of the rectangle is 5 centimeters less than six times its width, which can be expressed as 6w - 5. The formula for the area of a rectangle is length multiplied by width, so (6w - 5)w = 14. Simplifying this equation will give us a quadratic equation.
Expanding the equation: 6w^2 - 5w = 14.
Reordering: 6w^2 - 5w - 14 = 0.
After factoring or using the quadratic formula, we find possible solutions for 'w'. Substituting these solutions back into the original equation will give us the dimensions of the rectangle.