Solving for x in Parallelograms with the Same Perimeter

What does x equal? What is each parallelogram's perimeter?

The value of x is -1/2. The perimeter of the first parallelogram is 6 units, and the perimeter of the second parallelogram is 8 units.

Understanding the Solution:

The given problem involves two parallelograms with the same perimeter. We are provided with the dimensions of the parallelograms in terms of x and asked to find the value of x and the perimeter of each parallelogram. Finding the Value of x: Since the perimeters of the two parallelograms are equal, we can set up an equation based on the formula for the perimeter of a parallelogram, which is the sum of all its sides. For the first parallelogram: Perimeter = 2(2x + 4 + x) For the second parallelogram: Perimeter = 2(2x + 3x + 5) Setting these two expressions equal to each other: 2(2x + x + 4) = 2(5x + 5) Simplifying gives us: 6x + 8 = 10x + 10 Rearranging and solving for x: 4 = 4x x = -1/2 Calculating the Perimeter: Substitute x = -1/2 into the expressions for each parallelogram's perimeter to find the actual values. For the first parallelogram: Perimeter = 2((-1/2) + 4) = 6 units For the second parallelogram: Perimeter = 2((-1/2) + 5) = 8 units Therefore, the value of x is -1/2, and the perimeter of the first parallelogram is 6 units, while the perimeter of the second parallelogram is 8 units.
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