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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