Answer:
Perimeter = 1600 ft.
Explanation:
- The formula for the area of a rectangle is given by:
A = lw, where
- A is the area in units squared,
- l is the length,
- and w is the width.
Since we're told that the rectangle's length is three times its width, we can show this with the following equation:
l = 3w
Finding the width:
Now we can plug in 1200 for A and 3w for l in the rectangle area formula to find the width of the rectangle:
1200 = (3w)w
(1200 = 3w^2) / 3
√(400) = √(w^2)
200 = w
Thus, the width is 200 ft.
Finding the length:
Now we can plug in 200 for w in l = 3w to find the length:
l = 3(200)
l = 600
Thus, the length is 600 ft.
Finding the perimeter:
- The formula for the perimeter of a rectangle is given by:
P = 2l + 2w, where
- P is the perimeter,
- l is the length,
- and w is the width.
Thus, we can find the perimeter in ft by plugging in 600 for l and 200 for w in the perimeter formula:
P = 2(600) + 2(200)
P = 1200 + 400
P = 1600
Thus, the perimeter of the rectangle is 1600 ft.