Final answer:
To find the length and width of a rectangle given that its area is 1032 square yards and the width is 5 yards less than twice its length, set up the quadratic equation based on these conditions, solve for the length, and then calculate the width accordingly.
Step-by-step explanation:
The student is asked to find the measures of the length and width of a rectangle that has an area of 1032 square yards with the width being 5 yards less than twice the length. To solve this, let's denote the length of the rectangle as L yards. Therefore, the width will be 2L - 5 yards. Since the area of the rectangle is length times width, we have the equation:
L × (2L - 5) = 1032
Expanding and simplifying this equation gives us:
2L^2 - 5L - 1032 = 0
Now, we will solve this quadratic equation for L. This can be done either by factoring, using the quadratic formula, or computational methods. Upon solving this quadratic equation, you would find the positive value for L that satisfies the area equation, since a length can't be negative. With the value of L known, you can then calculate the width of the rectangle.
Step-by-Step:
- Assign variables: Let length be L and width be 2L - 5.
- Setup equation: L × (2L - 5) = 1032.
- Solve quadratic equation: Use appropriate methods to find the value of L.
- Calculate width: Substitute L into 2L - 5 to find the width.