a. 2 mm
b. 7 mm
c. 23 mm
d. 25 mm
Answer: WZ = 2 mm
Given the perimeter of parallelogram WXYZ as 50 millimeters, we can set up the equation for the perimeter as:
Perimeter = 2[(2x + 9) + (x - 5)]
50 = 2(3x + 4)
50 = 6x + 8
Now, solving for x:
6x = 50 - 8
6x = 42
x = 42 / 6
x = 7
Now, substituting x = 7 into the expression for WZ:
WZ = xy = x - 5 = 7 - 5 = 2 mm
Therefore, the correct answer is:
WZ = 2 mm
So, the correct option is:
b. 2 mm
Area and Perimeter of a Parallelogram
To find the area and perimeter of a parallelogram, you'll need to know the length of its base (b) and its height (h), as well as the length of its adjacent sides (a and b).
Area (A) of a Parallelogram:
The area of a parallelogram is calculated by multiplying the base (b) by the height (h).
A = base × height
Perimeter (P) of a Parallelogram:
The perimeter of a parallelogram is the sum of all its side lengths.
P = 2 × (side1 + side2)
Example: Let's assume we have a parallelogram with a base of 6 units, a height of 4 units, and the lengths of the adjacent sides are 5 units and 7 units.
-
Area: A = 6 × 4 = 24 square units
-
Perimeter: P = 2 × (5 + 7) = 2 × 12 = 24 units
So, for this parallelogram:
- Area = 24 square units
- Perimeter = 22 units
