Question

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.)

Answer 1

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

Answer 2

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

Answer 3

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?

Answer 4

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

Answer 5

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