## anonymous 4 years ago Please explain how to find the answer to me: 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? (The border must have equal width on each side.)

1. anonymous

$S=(3+2x)(5+2x)\quad,\quad x-\mbox{border width}$

2. anonymous

$(3+2x)(5+2x)\leq 19.25$$15+16x+4x^2\leq 19.25$$-4.25+16x+4x^2\leq 0$$-20.25+(4+2x)^2\leq 0$$(4+2x)^2\leq 20.25$$4+2x\leq 4.5$$x\leq 0.25$

3. anonymous

Why is it 2x instead of any other number? I mean in any other equation like this, would it be 2x as well or different? bc i have a whole test like this and I dont want to ask people every single question from the test... So how did you get the 2x or is 2 just standard in this equation?

4. anonymous

top border + bottom border=2x left-side border + right-side border=2x (all borders have width x)

5. anonymous

Ohh hehe yeaa i get it now lol that was a dumb question :/ lol thank you