Question 234475
P = 2L + 2W
A = LW


Solve for L in terms of W in the second equation.
Use that value of L in the first equation to solve for W.


Example:


2L + 2W = 100
LW = 400


Solve for L in second equation to get L = 400/W


Use that value in the first equation to get 2(400/W) + 2W = 100


Once you find W, then you go back to the first equation and solve for L


I'll do this one for you.


Equations are:


2L + 2W = 100
LW = 400


I use second equation to solve for L in terms of W to get L = W/400


I replace L with 400/W in the first equation to get:


2*(400/W) + 2*W = 100


I multiply both sides of this equation by W to get:


2*400 + 2*W*W = 100*W which becomes:


800 + 2W^2 = 100W


I subtract 100W from both sides of this equation and reorder the terms to get:


2W^2 - 100W + 800 = 0


I divide both sides by 2 to get:


W^2 - 50W + 400 = 0


I factor this quadratic equation to get:


(W-10) * (W-40) = 0


The result is that:


W = 10 or:
W = 40


I then go back to the first equation and use these values of W to solve for L.


I get:


L = 10 or:
L = 40


When L = 10, W = 40
When L = 40, W = 10


I confirm these values by substituting in the original equations of:


2L + 2W = 100
LW = 400


They confirm so the answers are good.


I get:


L = 10 or 40
W = 10 or 40
When L = 10, W = 40
When L = 40, W = 10