Answer:
L = 10 and W = 15
Explanation:
P = perimeter = 2L + 2W = 2(L+W)
P = 50
so...
L+W = 25
A = area = L*W
A = 150
That means we know:
L + W = 25
and
L*W =150
.
Substituting L = 25-W,
.
(25-W)*W = 150
25W -W^2 = 150
.
Add W^2 to both sides
.
25W = W^2 + 150
.
Subtract 25W from both sides
.
0 = W^2 - 25W + 150
.
Factoring
.
(W-10)(W-15) = 0
.
That means W can be either 10 or 15.
.
Since L = 25-W, L can be either 15 or 10, depending on W.
.
Either way the area is 150 because we know 10*15 = 15*10 = 150.
.
Answer:
L = 10 and W = 15
OR
L = 15 and W = 10
.
Done