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.