SOLUTION: If the length of the field is decreased by 3 meter and breadth is increased by 2 meter, then the area remains same. If the length and breadth is increased by 2 metre, then the are

Click here to see ALL problems on Equations

Question 188688: If the length of the field is decreased by 3 meter and breadth is increased by 2 meter, then the area remains same. If the length and breadth is increased by 2 metre, then the area is increased by 50 square meter. Find the length and breadth of the field.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
If the length of the field is decreased by 3 meters and breadth is increased
by 2 meters, then the area remains same. If the length and breadth is increased
by 2 meters, then the area is increased by 50 square meter. Find the length and
breadth of the field.
:
Let L = the original length to the field
Let W = the original width of the field
then
L*W = the original area
:
"If the length of the field is decreased by 3 meter and breadth is increased
by 2 meter, then the area remains same."
(L-3)*(W+2) = L*W
LW + 2L - 3W - 6 = LW
LW - LW + 2L - 3W = 6
2L - 3W = 6
:
"If the length and breadth is increased by 2 metre, then the area is increased
by 50 square meter."
(L+2)*(W+2) = LW + 50
LW + 2L + 2W + 4 = LW + 50
LW - LW + 2L + 2W = 50 - 4
2L + 2W = 46
:
Subtract the first equation from the above equation
2L + 2W = 46
2L - 3W = 6
-------------subtraction eliminates L
5W = 40
W =
W = 8 meters the original width
:
Use the 2nd equation to find L, substitute 8 for W:
2L + 2(8) = 46
2L = 46 - 16
2L = 30
L = 15 meters the original length
:
:
Check solution in the statement:
"If the length of the field is decreased by 3 meter and breadth is increased
by 2 meter, then the area remains same."
(15 - 3) * (8 + 2) = 15*8
12 * 10 = 120
:
You can check the solutions in the statement:
"If the length and breadth is increased by 2 meters, then the area is increased
by 50 square meter."
:
Any questions about this?