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Example:Quadratics - Rectangles Objective: Solve applications of quadratic equations using rectangles. An application of solving quadratic equations comes from the formula for the area of a rectangle. The area of a rectangle can be calculated by multiplying the width by the length. To solve problems with rectangles we will first draw a picture to represent the problem and use the picture to set up our equation. Example 1. The length of a rectangle is 3 more than the width. If the area is 40 square inches, what are the dimensions? 40 x We do not know the width,x. x +3 Length is 4 more, or x +4, and area is 40. x(x + 3)= 40 Multiply length by width to get area x 2 +3x = 40 Distribute − 40 − 40 Make equation equal zero x 2 + 3x − 40 =0 Factor (x − 5)(x + 8)=0 Set each factor equal to zero x − 5=0 or x + 8=0 Solve each equation +5+ 5 − 8 − 8 x =5 or x = − 8 Our x is a width, cannot be negative. (5)+ 3=8 Length is x +3,substitute 5 for x to find length 5 in by 8in Our Solution