The area of a rectangle can be found by multiplying its width by its length. In this case, we will divide the area by the width using polynomial long division to find the length of the rectangular room.
l r x + 6 & |l x^2 + 14 x + 48
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Divide
x^2/x= x
r x r x+6 & |l x^2+14 x+ 48
Multiply term by divisor
r x rl x+6 & |l x^2+14 x+ 48 & x^2+6x
Subtract down
r x r x+6 & |l 8x+48
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Divide
8x/x= 8
r x+8 r x+6 & |l 8x+48
Multiply term by divisor
rx+ 8 rl x+6 & |l 8x+48 & 8x+48
Subtract down
r x+8 r x+6 & |l 0
Therefore, the length of the rectangular room is (x+8) ft.
