SOLUTION: the widthof a piece is 4 metres less than is length. the air in the room is 165 m^2. find the length and breadth of this piece

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: the widthof a piece is 4 metres less than is length. the air in the room is 165 m^2. find the length and breadth of this piece      Log On


   

Question 125683: the widthof a piece is 4 metres less than is length. the air in the room is 165 m^2. find the length and breadth of this piece
Found 2 solutions by MathLover1, checkley71:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the width W of a piece is 4+m less than is length L:
W+=+L+-+4m
the aria A in the room is 165+m%5E2
find the length and breadth of this piece
given:
W+=+L+-+4m
A+=+165+m%5E2
since A+=+L%2AW, we will have:
165+m%5E2=+L%28L+-+4m%29
165+m%5E2=+L%5E2+-+4m%2AL
0=+L%5E2+-+4m%2AL+-+165+m%5E2
or
+L%5E2+-+4m%2AL+-+165+m%5E2+=+0 .....use quadratic formula to solve for L


x%5B1%2C2%5D+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+


x%5B1%2C2%5D+=+%284m+%2B-+sqrt%28+16m%5E2+%2B+660m%5E2+%29%29%2F2
x%5B1%2C2%5D+=+%284m+%2B-+sqrt%28+676m%5E2+%29%29%2F2
x%5B1%2C2%5D+=+%284m+%2B-+26m%29%2F2

x%5B1%5D+=+%284m+%2B+26m%29%2F2
x%5B1%5D+=++30m%2F2
x%5B1%5D+=++15m

x%5B2%5D+=+%284m+-+26m%29%2F2
x%5B2%5D+=++-22m%2F2
x%5B2%5D+=++-11m ....since this solution is a negative number, we will exclude this solution because the lenght coud be only positive number
so, the lenght is L+=+15m
then the width is
W+=+L+-+4m....plug in L
W+=+15m+-+4m
W+=+11m+

check the area:
A+=+L%2AW
A+=+15m%2A11m
A+=+165m%5E2




Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
COMMENT: AIR ISN'T USUALLY MEASURED IN SQUARE METERS. IF YOU HAD A THIRD MEASUREMENT FOR THE HEIGHT OF THE ROOM IT WOULD MAKE MORE SENSE.
HOWEVER I'LL TRY TO ANSWER THE PROBLEM AS PRESENTED.
W=L-4
L(L-4)=165
L^2-4L-165=0
(L-15)(L+11)=0
L-15=0
L=15 ANSWER.
WIDTH=15-4=11 ANSWER.
PROOF
15*11=165
165=165