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Example 10.41 from Elementary Algebra, 10.4 Solve Applications Modeled by Quadratic Equations
Solve Applications Modeled by Quadratic Equations: example 10.41
Mike wants to put 150 square feet of artificial turf in his front yard. This is the maximum area of artificial turf allowed by his homeowners association. He wants to have a rectangular area of turf with length one foot less than three times the width. Find the length and width. Round to the nearest tenth of a foot.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Step 1. Read the problem. Draw a picture. Step 2. Identify what we are looking for. We are looking for the length and width. Step 3. Name what we are looking for. Let the width of the rectangle.
the length of the rectangleStep 4. Translate into an equation.
We know the area. Write the formula for the area of a rectangle.Step 5. Solve the equation. Substitute in the values. Distribute. This is a quadratic equation, rewrite it in standard form. Solve the equation using the Quadratic Formula. Identify the a, b, c values. Write the Quadratic Formula. Then substitute in the values of a, b, c. Simplify. Rewrite to show two solutions. Approximate the answers using a calculator.
We eliminate the negative solution for the width.Step 6. Check the answer.
Make sure that the answers make sense.Step 7. Answer the question. The width of the rectangle is approximately 7.2 feet and the length 20.6 feet.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
The length of a 200 square foot rectangular vegetable garden is four feet less than twice the width. Find the length and width of the garden. Round to the nearest tenth of a foot.
How did it go?