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 piece 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.

Answer 1

The area of steel before cutting:

Area =
`(11+2x)*(6+2x)`cm²

=
`4x^(2)+22x+12x+66`

Hence, Area=
`4x^(2)+34x+66`

Area of steel after cutting out the 11*6 inside dimensions.

`4x^(2)+34x+66-(11*6)=4x^(2)+34x`

As the area should be close to 28 cm square, so equation becomes:

`4x^(2)+34x=28` or
`4x^(2)+34x-28=0`

Now for the answer, kindly see the image attached. It gives x=0.76

Hence, the answer is 0.76 cm.