Rectangle and a square shown below have the same perimeter. find the dimensions of each figure.

To find the dimensions of the rectangle and square with the same perimeter, we must first understand what perimeter means.

The perimeter is the total distance around the edge of a two-dimensional shape. For a rectangle, the perimeter (P) is the sum of twice the length (L) and twice the width (W): P = 2L + 2W. For a square, whose all sides (S) are equal, the perimeter is four times one side: P = 4S.

Given that both shapes have the same perimeter, you can set their perimeter formulas equal to each other to find the relationship between their dimensions.

Equating the two we get: 2L + 2W = 4S Dividing by 2, we simplify to: L + W = 2S This tells us that the sum of the length and width of the rectangle is equal to twice the side of the square.

Now, let's assume we have the perimeter value. To find the dimensions, we would need to have either (1) the length or the width of the rectangle or (2) the side of the square. With one of these values, we could solve for the rest. But without any numerical values or additional information, we cannot determine specific dimensions.

For example, if you know that the perimeter is 40 units, you would have:

Rectangle: 2L + 2W = 40 Square: 4S = 40

From the square's equation, you can find that S = 40 / 4, so S= 10 units.

Thus, the side of the square is 10 units long.

Using this value in the rectangle's equation, we get L + W = 2 * 10, so L + W = 20. Without loss of generality, if L were 12 units, then W would be 8 units, to make L + W = 20. There are many other possible pairs of values for L and W that would work, as long as their sum is 20.

Without specific information about one of the dimensions, we cannot provide exact measurements, but we can see that the process involves using the perimeter formulas to set up an equation and solve for the missing dimensions.