To find x and y, we need to equate the opposite sides of the parallelogram:
2x + y = 3y + 2x
4x - 3 = 5y - 8
Simplifying the first equation, we get:
2x - 2x = 3y - y
0 = 2y
Therefore, y = 0.
Using this value of y in the second equation:
4x - 3 = -8
4x = -8 + 3
4x = -5
x = -5/4
So, x = -5/4 and y = 0.
Now, let's find the perimeter of the parallelogram.
The length of one side of the parallelogram is 2x + y = 2(-5/4) + 0 = -5/2.
The length of the adjacent side is 4x - 3 = 4(-5/4) - 3 = -5 - 3 = -8.
The other two sides can be found using the same approach.
So, the perimeter of the parallelogram is:
Perimeter = (2)(-5/2) + (-8) + (3)(0) + (5)(0)
Perimeter = -5 - 8 + 0 + 0
Perimeter = -13 + 0 + 0
Perimeter = -13.
Therefore, the perimeter of the parallelogram is -13 cm.
Note: Typically, lengths and perimeters are expressed as positive values.
The sides of a pallelogram in fig 14.6 are given in cm with side is 2x+y, 4x-3, 3y+2x, 5y-8. Find x and y and the perimeter of the parallelogram
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1 answer