SOLUTION: A field, rectangular in shape, contains 64 square metres; if it were 4 metres longer and 3 metres narrower its area would be the same. Find its dimenstion. Please help me!!!!!!

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Question 761348: A field, rectangular in shape, contains 64 square metres; if it were 4 metres longer and 3 metres narrower its area would be the same. Find its dimenstion.
Please help me!!!!!!!!!!!!
Thank you
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A field, rectangular in shape, contains 64 square metres;
if it were 4 metres longer and 3 metres narrower its area
would be the same.
Find its dimension.
:
let L = original length
let W = original width
then
(L+4) = The "if" length
(W-3) = The "if" width
:
LW = 64
and
(L+4)(W-3) = 64
FOIL
LW - 3L + 4W - 12 = 64
LW - 3L + 4W - 12 - 64 = 0
LW - 3L + 4W - 76 = 0
Replace LW with 64
64 - 3L + 4W - 76 = 0
We have
4W - 3L - 12 = 0
4W = 3L + 12
divide by 4
W = .75L + 3
then replacing W in the original area equation (L*W)
L*(.75L+3) = 64
A quadratic equation
.75L^2 + 3L - 64 = 0
Solve for L using the quadratic formula: a=.75; b=3; c=-64
The positive solution ~ 7.45 is the length
:
Find the width: = 8.6 is width
:
See if that checks out
(7.45+4)*(8.6-3) ~ 64
:
The dimensions are not exact: L ~ 7.45; W ~ 8.6; is close