Loading…
Example 10.39 from Elementary Algebra, 10.4 Solve Applications Modeled by Quadratic Equations
Solve Applications Modeled by Quadratic Equations: example 10.39
An architect is designing the entryway of a restaurant. She wants to put a triangular window above the doorway. Due to energy restrictions, the window can have an area of 120 square feet and the architect wants the width to be 4 feet more than twice the height. Find the height and width of the window.
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 height and width. Step 3. Name what we are looking for. Let the height of the triangle.
the width of the triangleStep 4. Translate. We know the area. Write the formula for the area of a triangle. 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 equation. Then substitute in the values of a, b, c.. Simplify. Simplify the radical. Rewrite to show two solutions. Simplify. Since h is the height of a window, a value of does not make sense. The height of the triangle:
The width of the triangle:Step 6. Check the answer. Does a triangle with a height 10 and width 24 have area 120? Yes. Step 7. Answer the question. The height of the triangular window is 10 feet and the width is 24 feet. Notice that the solutions were integers. That tells us that we could have solved the equation by factoring.
When we wrote the equation in standard form, , we could have factored it. If we did, we would have solved the equation .
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Find the dimensions of a triangle whose width is four more than six times its height and has an area of 208 square inches.
How did it go?