Question

A steel company is making flat rectangular frames as a part of a new product they are launching Each frame will be cut out of a plece of steel

and will have a final area as close to 28 cm² as possible. The width of the frame needs to be uniform throughout. The inside dimensions of the

frame must be 11 cm by 6 cm.

Complete the equation that models the above situation, and find the width of the frame, x

Answer 1

The problem has no real solution, because the area of inside of the frame is bigger than the total area of the frame.

Explanation:

Any way here is the mathematical explanation/solve to this statement.

As show in the graphic, there is a representation of the situation stated in the problem. So in order to calculate the area we have the next equation as a function of x.

Area:

`A=b*h= (6+2x)(11+2x)\\\\A=28=66+12x+22x+4x^2}\\\\Simplifing\\\\4x^2+34x+38=0\\\\`

Solving the equation to find the roots (values of x):

`x=(-b+- √(b^2-4ac) )/(2a)=(-34+-√(546) )/(8)  \\\\solving\\\\x=-7.2\\\\x=-1.3\\`

So mathematically there is no real answer, since x is a width must be positive number. And practically the outer area must be bigger than the inner area, and the inner area is given by 6 times 11, or 66
`cm^2`.