Question

You work for a company that produces custom picture frames. A new customer needs to frame a piece of rectangular artwork with dimensions of 11 x 15 in. They don't want the framed art to be too big so they want to limit its area to 320 inches ^ 2. What should the width of the frame be to accommodate their wishes?

1) None of the choices are correct.

2) x² + 16 =800

3) x² + 8x + 16 = 800

4) x² 16x + 64 = 800

Answer 1

None of the choices are correct.

Explanation:

Let x be the width of the frame,

The framed art cannot me more than 320 square inches

`(11 + 2x) * (15+2x) \leq 320`

`(165 +30x +22x +4x^2 ) \leq 320`

`4x^2+52x + 165 \leq 320`

`4x^2 +52x + 165-320 \leq 0`

`4x^2 +52x - 155\leq 0`

By using the quadratic formula

`x = (-b\pm √((b^2-4ac)))/(2a)`

`x = (-52\pm √((52^2-4(4)(-155))))/(2(4))`

`x = (-52\pm √((2704+2480)))/(2(4))`

`x = (-52\pm √((5184)))/(2(4))`

`x = (-52\pm 72)/(2(4))`

`x = (20)/(8)`

`x= (5)/(2)`

`x = 2.5`

Frame must not be more than 2.5 inches wide.