Question

The plan for a city park shows that the park is a quadrilateral with straight paths along the diagonals. For what values of the variables is the park a parallelogram? In this case, what are the values of x and y?

Answer 1

Picture relating to question has been attached below

Answer:

x = 10 ; y = 15

Explanation:

The values for which the park is a parallelogram :

For the quadrilateral to be a parallelogram ; the diagonals will bisect each other such as :

VT = RV and UV = VS

From the diagram :

VT = 3x + 5y

RV = 6x + 3y

UV = 11y + 33 m

VS = 14y - 12 m

VT = RV and UV = VS

3x + 5y = 6x + 3y

3x - 6x = 3y - 5y

-3x = - 2y

3x = 2y

11y + 33 = 14y - 12

11y - 14y = - 12 - 33

-3y = - 45

y = 45/3

y = 15

From ;

3x = 2y

3x = 2*15

3x = 30

x = 30/3

x = 10