EXAMPLE 1 In-Class Example 1 A rectangular vegetable garden is 4 ft longer than it is wide. What are the dimensions if it covers 60 sq ft? Answer: length 10 ft, width 6 ft YOU TRY 1 1 Solve Problems Involving Geometry A builder must cut a piece of tile into a right triangle. The tile will have an area of 40 in2, and the height will be 2 in. shorter than the base. Find the base and height. Solution Step 1: Read the problem carefully. Draw a picture. Step 2: Choose a variable to represent the unknown. b b 2 b the base b 2 the height Step 3: Translate the information that appears in English into an algebraic equation. We are given the area of a triangular-shaped tile, so let’s use the formula for the area of a triangle and substitute the expressions above for the base and the height and 40 for the area. Area 1 2 (base)(height) 40 1 2 (b)(b 2) Substitute Area 40, base b, height b 2. Step 4: Solve the equation. Eliminate the fraction fi rst. 80 (b)(b 2) Multiply by 2. 80 b2 2b Distribute. 0 b2 2b 80 Write the equation in standard form. 0 (b 10)(b 8) Factor. b 10 0 or b 8 0 Set each factor equal to zero. b 10 or b 8 Solve. Step 5: Check the answer, and interpret the solution as it relates to the problem. Since b represents the length of the base of the triangle, it cannot be a negative number. So, b 8 cannot be a solution. Therefore, the length of the base is 10 in., which will make the height 10 2 8 in. The area, then, is 1 2 (10)(8) 40 in2. The height of a triangle is 3 cm more than its base. Find the height and base if its area is 35 cm2. 2 Solve Problems Involving Consecutive Integers In Chapter 2, we solved problems involving consecutive integers. Some applications involving consecutive integers lead to quadratic equations. www.mhhe.com/messersmith SECTION 7.6 Applications of Quadratic Equations 433
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