Of all rectangles that can be formed from thirty 4 x 4 squares, the one with the greatest perimeter has a perimeter of -----------?
Ignore the fact that each tile is 4x4, it could just as well be 1x1.
The important data is that we have 30 of them to be arranged in a rectangle, there are only 4 possible ways to do this.
Form a chart with s1 - side1, s2 - side2, p - perimeter
s1 s2 p
1 30 62
2 15 34
3 10 26
5 6 22
clearly 62 is the largest perimeter for a 1x1, so for our 4x4 it would be 4x62 or 248
OMG thank u so much
To find the rectangle with the greatest perimeter, we need to maximize the length and width while still using all thirty 4 x 4 squares.
Let's start by figuring out the dimensions of the rectangle.
Since we have thirty 4 x 4 squares, the total area of all the squares is equal to the area of the rectangle.
The area of one square is 4 x 4 = 16 square units.
The total area of all thirty squares is 30 x 16 = 480 square units.
To find the dimensions of the rectangle, we need to factorize the area of 480:
480 = 8 x 60
480 = 10 x 48
480 = 12 x 40
480 = 16 x 30
480 = 20 x 24
Notice that the pair with the greatest sum is 20 x 24.
Therefore, the rectangle with the greatest perimeter has dimensions 20 x 24.
To find the perimeter, we use the formula:
Perimeter = 2 * (length + width)
Perimeter = 2 * (20 + 24)
Perimeter = 2 * (44)
Perimeter = 88
Hence, the rectangle with the greatest perimeter has a perimeter of 88 units.
To find the rectangle with the greatest perimeter that can be formed from thirty 4x4 squares, we need to understand the concept of perimeter.
Perimeter is the total length of the boundaries or outer edges of the shape. For a rectangle, the perimeter is found by adding the lengths of all four sides.
In this case, we have thirty 4x4 squares. Since a single 4x4 square has sides measuring 4 units in length, we can multiply the side length by the number of squares to find the total length of one side of the rectangle.
Total length of one side = 4 (side length of a square) x 30 (number of squares) = 120 units
Since a rectangle has two pairs of equal sides, we can calculate the perimeter by multiplying the total length of one side by 2.
Perimeter of the rectangle = Total length of one side x 2 = 120 units x 2 = 240 units
Therefore, the rectangle with the greatest perimeter that can be formed from thirty 4x4 squares has a perimeter of 240 units.