We are given a rectangular shape. The length is 3 times larger than its width. What this means is if the width were 4 inches, the length would be 12 (since 12 is 3 times larger than 4).
The perimeter formula for a rectangle is P = 2*(length) + 2*(width)
Let's say width = x. Since the length is 3 times larger than the width, that would mean that length = 3x. Let's plug these into the equation.
P = 2*(3x) + 2*(x) = 6x + 2x = 8x
The question already gives a value for the perimeter, which is 144 cm. So if 8x and 144 are the exact same perimeter for this rectangular field, we can set them equal to each other to find x.
8x = 144
x = 18
So now we can use this information to find the area of the rectangle. The area formula for a rectangle is A = (length) * (width).
A = (3x) * (x) = 3x^2
Plug in 18 for x.
A = 3(18)^2 = 3 * 18 * 18 = 3 * 324 = 972 cm^2.