Question 998912: Please help me because I have done this problem over and over. I have never been good at math. Please show all steps. Thanks
3. For a student recreation building at Northland Community College, an architect wants to lay out a rectangular piece of land that has a perimeter of 204m and an area of 2565m^2. Find the dimensions of the land (Hint: write a system of two equations, then solve the system.)
After I did it my answer I came up with was 125m^2
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
L = length of rectangle
W = width of rectangle
A = area of rectangle
P = perimeter of rectangle
A = L*W
P = 2*(L+W)
"perimeter of 204m" ---> P = 204
"area of 2565m^2" ----> A = 2565
P = 2*(L+W)
204 = 2*(L+W) ... plug in P = 204
204/2 = 2*(L+W)/2 ... Divide both sides by 2.
102 = L+W
L+W = 102
L+W-W = 102-W ... Subtract W from both sides.
L = 102-W
A = L*W
2565 = L*W ... plug in A = 2565
2565 = (102-W)*W ... replace L with 102-W
2565 = W*(102-W)
2565 = W*102+W*(-W)
2565 = 102W-W^2
2565-2565 = 102W-W^2-2565 ... Subtract 2565 from both sides.
0 = 102W-W^2-2565
-W^2+102W-2565 = 0
Use the quadratic formula to solve the last equation above to get W = 45 or W = 57
If W = 45, then
L = 102-W
L = 102-45
L = 57
If W = 57, then
L = 102-W
L = 102-57
L = 45
So we see that the dimensions of this rectangle are 57 meters by 45 meters
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