Answer:
Area of rectangle (A) is given by:
[tex]A = lw[/tex]
where, l is the length and w is the width of the rectangle.
As per the statement:
The area of a room is 396 square feet.
The length is (x + 8) feet and the width is (x + 4) feet.
⇒A = 396 square feet , l = (x+8) feet and w = (x+4) feet
Substitute these given values we have;
[tex]396 = (x+8)(x+4)[/tex]
⇒[tex]396 = x^2+4x+8x+32[/tex]
Combine like terms;
⇒[tex]396 = x^2+12x+32[/tex]
Subtract 32 from both sides we have;
[tex]364 = x^2+12x[/tex]
or
[tex]x^2+12x-364 =0[/tex]
⇒[tex]x^2+26x-14x-364 = 0[/tex]
⇒[tex]x(x+26)-14(x+26)=0[/tex]
⇒[tex](x+26)(x-14) = 0[/tex]
By zero product property we have;
x+26 = 0 or x-14 = 0
⇒x = -26 and x = 14
Since, side cannot be in negative.
⇒x = 14
then;
l = x+8 = 14+8 = 22 feet
w = x+4 = 14+4 = 18 feet
Therefore, the dimensions of the room are:
l = 22 feet and w = 18 feet
