Question

Solving a word problem using a quadratic equation with rationa... The length of a rectangle is 3ft more than twice the width, and the area of the rectangle is 77ft². Find the dimensions of the rectangle.

Answer 1

To find the dimensions of the rectangle, set up an equation based on the given information. Solve the quadratic equation to find the width and length of the rectangle.

Step-by-step explanation:

To find the dimensions of the rectangle, let's assume that the width of the rectangle is 'w'. According to the problem, the length of the rectangle is 3ft more than twice the width, which can be represented as 2w + 3. The area of the rectangle is given as 77ft², so we can set up the equation:

w * (2w + 3) = 77

Simplifying the equation, we get 2w² + 3w - 77 = 0. We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Solving the equation, we find that the width of the rectangle is 7ft and the length is 17ft.