# Four Questions Need Help With

• Jan 10th 2008, 07:59 PM
nathan02079
Four Questions Need Help With
1 . A farmer has rectangular garden plot surrounded by $\displaystyle 200ft$ of fence. Find the length and width of the garden if its is $\displaystyle 2400ft^2$.

2. Find the length of X if the shaded area is $\displaystyle 160 in^2$.
ImageShack - Hosting :: 59310350aa9.png

3. Find the length X if the shaded area is $\displaystyle 1200cm^2$
ImageShack - Hosting :: 22151047zo3.png

4. A cylindrical can has a volume of $\displaystyle 40\pi cm^3$ and is 10cm tall. What is the diameter?

Thanks a lot!
Nate
• Jan 10th 2008, 08:29 PM
SengNee
1)

$\displaystyle 2l+2w=200$
$\displaystyle l+w=100$
$\displaystyle l=100-w$......i

$\displaystyle A=2400$
$\displaystyle lw=2400$......ii

Substitute i into ii

$\displaystyle (100-w)w=2400$[/tex]
$\displaystyle 100w-w^2=2400$
$\displaystyle w^2-100w+2400=0$
$\displaystyle (w-40)(w-60)=0$

If $\displaystyle w=40$,
Therefore, $\displaystyle l=60$.

If $\displaystyle w=60,$
Therefore, $\displaystyle l=40$.

2) I can't see the shaded region.

$\displaystyle A=160$
$\displaystyle (x+13)(x+14)-(13)(14)=160$
$\displaystyle x^2+27x+182-182=160$
$\displaystyle x^2+27x-160=0$
$\displaystyle (x+32)(x-5)=0$

$\displaystyle x=-32$
$\displaystyle x=5$

$\displaystyle x>0$
Therefore, $\displaystyle x=5$.

3) I can't see the shaded region.

$\displaystyle A=0.5bh$
$\displaystyle 1200=0.5[(x+1)+(1)](x)$
$\displaystyle 2400=x^2+2x$
$\displaystyle x^2+2x-2400=0$
$\displaystyle (x-48)(x+50)=0$

$\displaystyle x=48$
$\displaystyle x=-50$

$\displaystyle x>0$
Therefore, $\displaystyle x=48$.

4)

$\displaystyle V=\pi r^2h$
$\displaystyle 40\pi=\pi r^2(10)$
$\displaystyle r^2=4$
$\displaystyle r=±2$

$\displaystyle r>0$
Therefore,
$\displaystyle r=2$
$\displaystyle 2r=4$
$\displaystyle d=4$