Answer:
The room has a length of 27 feet and width 15 feet.
Step-by-step explanation:
Given that:
Area of den = A = 405 square feet
Let,
L represent the length of room and W represent the width of room.
L = W+12
Area = Length * Width
[tex]405=(W+12)*W\\405=W^2+12W\\W^2+12W-405=0[/tex]
Factorizing the equation
[tex]W^2-15W+27W-405=0\\W(W-15)+27(W-15)=0\\(W-15)(W+27)=0\\[/tex]
Either,
W-15 = 0
W=15
Or,
W+27=0
W=-27
As the width cannot be negative, therefore,
Width of den = 15 feet
Length of den = 15+12 = 27 feet
Hence,
The room has a length of 27 feet and width 15 feet.
