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.