# Four Questions Need Help With

• Jan 10th 2008, 08:59 PM
nathan02079
Four Questions Need Help With
1 . A farmer has rectangular garden plot surrounded by $200ft$ of fence. Find the length and width of the garden if its is $2400ft^2$.

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

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

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

Thanks a lot!
Nate
• Jan 10th 2008, 09:29 PM
SengNee
1)

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

$A=2400$
$lw=2400$......ii

Substitute i into ii

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

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

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

2) I can't see the shaded region.

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

$x=-32$
$x=5$

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

3) I can't see the shaded region.

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

$x=48$
$x=-50$

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

4)

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

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