Your company is going to make frames as part of a new product they are launching.
The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be # 28 cm^2#
The inside of the frame has to be 11 cm by 6 cm
What should the width x of the metal be?
Area of steel before cutting:
Area = #(11 + 2x) × (6 + 2x) cm^2#
Area = #66 + 22x + 12x + 4x^2#
Area = #4x^2 + 34x + 66#
Area of steel after cutting out the 11 × 6 middle:
Area = # + 34x + 66 - 66#
Area = #4x^2 + 34x#
Let us solve this one graphically!
Here is the graph of 4x2 + 34x :
The desired area of 28 is shown as a horizontal line.
The area equals 28 cm2 when:
x is about -9.3 or 0.8
The negative value of x make no sense, so the answer is:
x = 0.8 cm (approx.)
You can try it out yourself and find the roots of the quadratic equation using the quadratic formula
# x = [ -b ± sqrt(b^2 - 4ac) ] / (2a#
There are many more examples at http://www.mathsisfun.com/algebra/quadratic-equation-real-world.html