Math Problem Statement
The area of a rectangle is 28 yd², and the length of the rectangle is 5 yd less than three times the width. Find the dimensions of the rectangle.
Solution
In this problem, we are told that the area of a rectangle is 28 square yards, and the length is 5 yards less than three times the width. We need to find the dimensions of the rectangle.
Let:
- represent the width of the rectangle.
- represent the length of the rectangle.
We are given the following information:
- The length is 5 yards less than three times the width, so:
- The area of the rectangle is 28 square yards, and the area is calculated as . Thus:
Substitute the expression for from the first equation into the second equation: Expand and simplify:
This is a quadratic equation. We can solve it using the quadratic formula: Simplify:
So, can be: or [ w = \frac{5 -
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Quadratic Equations
Formulas
Area of a rectangle: Area = length × width
Quadratic equation: ax^2 + bx + c = 0
Theorems
Quadratic formula
Suitable Grade Level
Grades 8-10