Question 57024
The length of a room is 4 metres longer than its width. The height of the room
is 3 metres  and its volume is 1000m^3. Find the length and width of the room. 
The formula for the volume of a rectangular solid is:{{{highlight(V=L*W*H)}}}
Height (h)=3 m
Width (W)=x
Length (L)=(x+4)
Volume (V)=1000 m^3
{{{1000=3x(x+4)}}}
{{{1000-1000=3x(x+4)-1000}}}
{{{0=3x(x+4)-1000}}}
{{{0=3x^2+12x-1000}}}
This is in standard form:  {{{ax^2+bx+c}}}
a=3, b=12, and c=-1000
Use the quadratic formula:{{{highlight(x=(-b+-sqrt(b^2-4ac))/(2a))}}}
{{{x=(-(12)+-sqrt((12)^2-4(3)(-1000)))/(2(3))}}}
{{{x=(-12+-sqrt(144+12000))/6}}}
{{{x=(-12+-sqrt(12144))/6}}}
We can ignore the negative value, beacuse this is a dimension.
{{{x=(-12+sqrt(12144))/6}}}
{{{x=(-12+4sqrt(759))/6}}}
{{{x=4(-3+sqrt(759))/6}}}
{{{x=2(-3+sqrt(759))/3}}}
x is approximately 16.36663642
The Width (W): x=16.3666 m round off to whatever your teacher asks for.
The length (L): x+4=16.3666+4=20.3666 m
Happy Calculating!!!