Question

Find the value of x and y from the following parallelogram:

Answer 1

Given:

Parallelogram with side labels:

Top = 2y + 2

Bottom = 3x

Left = 2y – 5

Right = x + 1

Opposite sides of a parallelogram are equal.

Step-wise calculation:

1. From opposite sides:

Bottom = Top

3x = 2y + 2   ...(Equation 1)

2. The other pair:

Left = Right

2y – 5 = x + 1   ...(Equation 2)

3. Solve (Equation 2):

2y – 5 = x + 1

⇒ 2y = x + 6

⇒ `y = (x + 6)/2`

4. Substitute into (Equation 1):

3x = 2y + 2 

= `2 xx ((x + 6)/2) + 2`

= (x + 6) + 2

= x + 8

5. So, 3x = x + 8

⇒ 2x = 8

⇒ x = 4

6. Then `y = (4 + 6)/2`

= `10/2`

= 5