SOLUTION: The length of a room is 4 metres longer than its width. The height of the room is 3 metres and its volume is 1000m3. Find the length and width of the room.

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Question 57024This question is from textbook Oxford mathematics for the Caribbean
: The length of a room is 4 metres longer than its width. The height of the room
is 3 metres and its volume is 1000m3. Find the length and width of the room. This question is from textbook Oxford mathematics for the Caribbean

Answer by funmath(2925) About Me  (Show Source):
You can put this solution on YOUR website!
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%28V=L%2AW%2AH%29
Height (h)=3 m
Width (W)=x
Length (L)=(x+4)
Volume (V)=1000 m^3
1000=3x%28x%2B4%29
1000-1000=3x%28x%2B4%29-1000
0=3x%28x%2B4%29-1000
0=3x%5E2%2B12x-1000
This is in standard form: ax%5E2%2Bbx%2Bc
a=3, b=12, and c=-1000
Use the quadratic formula:highlight%28x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29%29
x=%28-%2812%29%2B-sqrt%28%2812%29%5E2-4%283%29%28-1000%29%29%29%2F%282%283%29%29
x=%28-12%2B-sqrt%28144%2B12000%29%29%2F6
x=%28-12%2B-sqrt%2812144%29%29%2F6
We can ignore the negative value, beacuse this is a dimension.
x=%28-12%2Bsqrt%2812144%29%29%2F6
x=%28-12%2B4sqrt%28759%29%29%2F6
x=4%28-3%2Bsqrt%28759%29%29%2F6
x=2%28-3%2Bsqrt%28759%29%29%2F3
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!!!