SOLUTION: For a building at Hertiage college , an architect wants to layout a rectangle piece of ground that has a perimeter of 204 metres and area of 2565 metres squared .Find the dimension

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Question 808175: For a building at Hertiage college , an architect wants to layout a rectangle piece of ground that has a perimeter of 204 metres and area of 2565 metres squared .Find the dimensions of the ground.
Can you please help me out? Thank you
Found 2 solutions by JBarnum, richwmiller:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
length times width equals area
length plus length plus width plus width equals perimeter
so:
LW=A
2L%2B2W=P OR 2%28L%2BW%29=P
A=2565
P=204
.
LW=2565
AND
2%28L%2BW%29=204
%28L%2BW%29=102
L=102-W
USE ABOVE IN FIRST EQUATION
%28102-W%29W=2565 DISTRIBUTE
-W%5E2%2B102W=2565 PUT IN QUADRATIC FORM AND MULTIPLY BY -1
W%5E2-102W%2B2565=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 1W%5E2%2B-102W%2B2565+=+0) has the following solutons:

W%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-102%29%5E2-4%2A1%2A2565=144.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--102%2B-sqrt%28+144+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%28-102%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+57
W%5B2%5D+=+%28-%28-102%29-sqrt%28+144+%29%29%2F2%5C1+=+45

Quadratic expression 1W%5E2%2B-102W%2B2565 can be factored:
1W%5E2%2B-102W%2B2565+=+1%28W-57%29%2A%28W-45%29
Again, the answer is: 57, 45. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-102%2Ax%2B2565+%29

W=57ORW=45
IF W=57 THEN L=102-57L=45
IF W=45 THEN L=102-45L=57
CHECK
45%2A57=2565
45%2B45%2B57%2B57=204
SINCE LENGTH IS TYPICALLY A GREATER NUMBER THEN THE WIDTH ID GO WITH highlight%28L=57%29 AND highlight%28W=45%29

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
2x+2y=204,
x*y=2565
x = 45, y = 57
or
x = 57, y = 45