Step-by-step explanation:
Let l be the length of the room, and w be the width.
If the length is 6 feet longer than twice the width, then we can say l = 2w+6
Knowing that the formula for the perimeter of a rectangle is P = 2l+2w, and knowing that P=144 ft, we can say that 2L + 2w= 144 ft.
To find the dimensions, we plug our value for l into our perimeter equation
This gives us the following equation: 144= 2(2w+6) + 2w, which simplifies to 144=4w+12+2w, which further simplifies to 144= 6w+12
To get w on one side of the equation, we subtract 12 from each side, which gives us 132=6w
Dividing each side by 6, we determine that w= 22 ft.
Plugging this value back into our first equation we see that l= 2(22)+6
So l= 50 ft.
So, the dimensions of the room are as follows: length is 50 ft., width is 22 ft.
