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

Answer 1

Answer:

$4x^2+34x-28=0$

x = 0.76

Step-by-step explanation:

We can write the area of steel before it is cut as:

Area = $(11+2x)*(6+2x)cm^2$

Expanding it by multiplying the brackets to get:

Area = $4x^2+22x+12x+66$

Area  area of steel before cutting = $4x^2+34x+66$

Then we need the area of steel after 11*6 inside dimensions are cut out:

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

This area should be close to 28 cm$^2$, hence the equation becomes:

$4x^2+34x-28=0$

Moreover, plotting the graph gives us a value of x = 0.76.