Question
A parallelogram of sides 2x+y,3y+2x 2 ,5y-8,4x-3
Answers
GPT 3.5
To determine whether a quadrilateral with sides of lengths 2x+y, 3y+2x, 5y-8, and 4x-3 is a parallelogram, we need to check if opposite sides are equal in length and parallel to each other.
Given sides:
- 2x + y
- 3y + 2x
- 5y - 8
- 4x - 3
For a parallelogram, opposite sides must be equal in length and parallel. Let's check if this condition is satisfied:
1. Sides 2x + y and 5y - 8:
2x + y = 5y - 8
Rearrange: 2x - 5y = -8 - y
There is no way to simplify or equate these two sides as they involve variables that are not directly related. So, they may or may not be equal.
2. Sides 3y + 2x and 4x - 3:
3y + 2x = 4x - 3
Rearrange: 2x - 4x = -3 - 3y
-2x = -3 - 3y
2x = 3 + 3y
x = 3/2 + 3/2y
The sides 3y + 2x and 4x - 3 are not equal. Therefore, the given sides do not form a parallelogram.
Given sides:
- 2x + y
- 3y + 2x
- 5y - 8
- 4x - 3
For a parallelogram, opposite sides must be equal in length and parallel. Let's check if this condition is satisfied:
1. Sides 2x + y and 5y - 8:
2x + y = 5y - 8
Rearrange: 2x - 5y = -8 - y
There is no way to simplify or equate these two sides as they involve variables that are not directly related. So, they may or may not be equal.
2. Sides 3y + 2x and 4x - 3:
3y + 2x = 4x - 3
Rearrange: 2x - 4x = -3 - 3y
-2x = -3 - 3y
2x = 3 + 3y
x = 3/2 + 3/2y
The sides 3y + 2x and 4x - 3 are not equal. Therefore, the given sides do not form a parallelogram.