The length of a rectangle is four times its width. If the area of the rectangle is 324m^2, find its perimeter.

Step-by-step explanation:

We know that the length is four times the width, so:

We also know the area, which is 324 m². The formula for area:

Insert the known values:

Solve for w. Simplify by removing parentheses:

Divide 4 from both sides to isolate the variable:

Find the square root of both sides:

The width is 9 m.

We know the width. Now find the length by using the area formula and inserting known values:

Solve for l. Divide both sides by 9:

The length of the rectangle is 36. (You can check: 4 times 9 is 36)

Now find the perimeter:

Insert values:

The perimeter is 90 m.