Given the perimeter of the parallelogram in the image below is 60, the value of GH will be: 23.
Recall:
- Perimeter of a parallelogram = 2(a + b), where a is the side length and b is the base length.
- Opposite sides of a parallelogram are equal.
Given the parallelogram as shown in the diagram below, where:
base (b) = EF = 5x + 18
side (a) = HE = 3x + 4
Perimeter = 60
Plug in the values into the formula:
60 = 2[(3x + 4) + (5x + 18)]
60 = 2[3x + 4 + 5x + 18]
60 = 2[8x + 22]
60 = 16x + 44
60 - 44 = 16x
16 = 16x
1 = x
x = 1
GH = EF = 5x + 18 (equal opposite sides of parallelogram)
GH = 5x + 18
GH = 5(1) + 18
GH = 23
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