Question 998912

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 <font color="red">57 meters by 45 meters</font>