Alexei wants to hang a mirror in his boat but the mirror and frame must not have an area larger than 19.25 square feet. The mirror is 3 feet wide and 5 feet long. Which quadratic equation represents the area of the mirror and frame combined?

Sep 26, 2016

$4 {x}^{2} + 16 x - 4.25 \le 0$

Explanation:

The area of a rectangle is $A = l \times b$

However, the lengths that are given for the mirror do not include the frame, which we will assume is the same width on all sides.

Let the width of the frame be $x$.
The width of the frame = 3+2x "larr there is a frame on each side
The length of the frame $= 5 + 2 x$

$\left(3 + 2 x\right) \left(5 + 2 x\right) \le 19.25$

$15 + 6 x + 10 x + 4 {x}^{2} - 19.25 \le 0$

$4 {x}^{2} + 16 x - 4.25 \le 0$