Final answer:
To solve the word problem, set up a quadratic equation using the given information. Solve the quadratic equation to find the width of the rectangle. Substitute the width into the expression for the length to find the dimensions of the rectangle.
Step-by-step explanation:
Solving a word problem using a quadratic equation
To solve this problem, let's represent the width of the rectangle as x. The length of the rectangle can be expressed as 2x - 1 since it is 1 yard less than double the width. The area of the rectangle is given as 21 yd², so we can set up the quadratic equation x(2x - 1) = 21. Using the zero-product property, we can solve this equation to find the value of x, which represents the width of the rectangle. Once we have the value of x, we can find the length of the rectangle by substituting it into the expression 2x - 1.
Example:
Let's solve the equation x(2x - 1) = 21. First, rewrite the equation as 2x² - x - 21 = 0. Factor the quadratic equation as (2x + 7)(x - 3) = 0. Setting each factor equal to zero, we find 2x + 7 = 0 or x - 3 = 0. Solving these linear equations, we get x = -3.5 or x = 3. Since the width cannot be negative, we discard x = -3.5. Therefore, the width of the rectangle is x = 3 yards. Substituting this value into the expression 2x - 1, we find the length of the rectangle to be 2(3) - 1 = 5 yards. So, the dimensions of the rectangle are 3 yards by 5 yards.
Learn more about Solving a word problem using a quadratic equation with rational roots