# Rectangular room has width twice of its length When 6 is decreased from both length and width then its area is differed by 108 so find the width?

The width of the room is equal to twice the Length. Suppose Length = L, width = W, and A = area

W = 2L from the information in the question

Now we know area, A is equal to length times width

W*L=A, plug in 2L for W and we get 2L*L=A or
*2L^2=A*

Next, we see that when 6 is subtracted from both length and width A becomes 108 less.

So (2L-6)*(L-6)=A-108

Multiply (2L-6)*(L-6) out and the result is (2L^2-18L+36) Set that equal to A-108

(2L^2-18L+36)=A-108. We found out that A=2L^2 earlier so we can substitute the terms.

(2L^2-18L+36)=2L^2-108. Now solve for L

Subtract 2L^2 from both sides

(-18L+36)=(-108)

Subtract 36 from both sides

(-18L)=(-144)

Divide by (-18)

L=8

We know W=2L so W=16

Now lets test our answer.

16*8=128

(16-6)*(8-6)=10*2=20

128-20=108

So the answer of L=8 and W=16 is correct.