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.
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
Subtract 36 from both sides
Divide by (-18)
We know W=2L so W=16
Now lets test our answer.
So the answer of L=8 and W=16 is correct.