Question 256781
let L = length and W = width.


area = L*W


(L+1)*(W+1) = 84


(L-1)*(W-1) = 48


multiply these out to get:


LW + L + W + 1 = 84
LW - L - W + 1 = 48


add both these equations together to get:


2LW + 2 = 132


subtract 2 from both sides of these equations to get:


2LW = 130


divide both sides of these equations by 2 to get:


LW = 65


substitute for LW in the original 2 equations to get:


LW + L + W + 1 = 84
LW - L - W + 1 = 48


become:


65 + L + W + 1 = 84
65 - L - W + 1 = 48


subtract 66 from both sides of these equations to get:


L + W = 18
-L -W = -18


Solve for L in each equation to get:


L = 18 - W (same answer for each equation).


You have a value for L in relation to W.


substitute for L in the first original equation to get:


(L+1)*(W+1) = 84 becomes:


(18-W+1) * (W+1) = 84


simplify each factor to get:


(19-W) * (W + 1) = 84


multiply out the factors to get:


19W + 19 - W^2 - W = 84


combine like terms to get:


-W^2 + 18W + 19 = 84


subtract 84 from both sides of the equation to get:


-W^2 + 18W - 65 = 0


multiply both sides of the equation by -1 to get:


W^2 - 18W + 65 = 0


factor to get:


(W-13) * (W - 5) = 0


you get:


W = 13 or W = 5


since L = 18 - W, then you also get:


When W = 13, L = 5
When W = 5, L = 13


substitute these values in the original equations to get:


When W = 13 and L = 5, then:


(L+1)*(W+1) = 84
(L-1)*(W-1) = 48


become:


6*14 = 84
4*12 = 48


When W = 5 and L = 13, then:


(L+1)*(W+1) = 84
(L-1)*(W-1) = 48


become:


14*6 = 84
12*4 = 48


all equations are true so the values for L and W are good.


Perimeter = 2L + 2W.


When L = 5 and W = 13, perimeter becomes 10 + 26 = 36


When L = 13 and W = 5, perimeter becomes 26 + 10 = 36


your answer is:


perimeter = 36