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A bedroom door has a perimeter of feet and an area of square feet. What are the dimensions of the door? feet by feet
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Q. A bedroom door has a perimeter of feet and an area of square feet. What are the dimensions of the door? feet by feet
- Perimeter Equation: Let's denote the length of the door as and the width as . The perimeter of a rectangle is given by the formula . Since we know the perimeter is feet, we can write the equation .
- Simplify Perimeter Equation: To simplify the equation, we can divide both sides by , which gives us .
- Area Equation: The area of a rectangle is given by the formula . We know the area is square feet, so we can write the equation .
- Solve System of Equations: We now have a system of two equations with two variables:. . We can solve this system by expressing one variable in terms of the other using the first equation. Let's solve for : .
- Substitute Width: Substitute from the previous step into the area equation: .
- Expand Equation: Expand the equation: .
- Rearrange Equation: Rearrange the equation to form a quadratic equation: .
- Factor Quadratic Equation: Factor the quadratic equation: l - \(10)(l - ) = \
- Solve for Length: Set each factor equal to zero and solve for : or , which gives us or .
- Possible Dimensions: Since and are interchangeable in a rectangle (one can be the length and the other the width), we have two possible dimensions for the door: feet by feet or feet by feet.
