Mari has 39 square feet of patio bricks. Each square brick has side 1 foot long. What is the greatest perimeter of a rectangle that she can make with the bricks?

80 ft

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The answer is 80ft

To find the greatest perimeter of a rectangle that Mari can make with the given bricks, we need to first determine the dimensions of the rectangle.

Since each brick is a square with a side length of 1 foot, we can start by finding the total number of bricks Mari has. To do this, we divide the total square footage of patio bricks (39 square feet) by the area of a single brick (1 square foot). Therefore, Mari has 39/1 = 39 bricks.

Now, let's try to find the dimensions that will result in the greatest perimeter. To maximize the perimeter, we want to minimize the number of sides with length 1 foot. Since the bricks are all square, we can have at most two sides of 1 foot.

If we lay the bricks out in a rectangle with one side length of 1 and the other side length of 19 (39 divided by 2), we would have a perimeter of 2(1+19) = 2(20) = 40 feet.

Similarly, if we lay the bricks out in a rectangle with one side length of 2 and the other side length of 18, we would have a perimeter of 2(2+18) = 2(20) = 40 feet.

In general, we can see that the perimeter will be maximized when the two side lengths are as close to each other as possible. So, using the 39 bricks, the greatest perimeter Mari can make with the bricks is 40 feet.