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 lengths of the paths?

Answer 1

• x = 10, y = 15
• RT = 210 m, US = 396 m

Explanation:

Diagonals of parallelogram bisect each other;

• UV = VS and
• RV = VT

Substitute values:

11y + 33 = 14y - 12 ⇒ 14y - 11y = 33+12 ⇒ 3y = 45 ⇒ y = 15

• US = 2(11*15+33) = 396 m

3x + 5y = 6x + 3y ⇒ 6x - 3x = 5y - 3y ⇒ 3x = 2y ⇒ 3x = 30 ⇒ x = 10

• RT = 2(3*10 + 5*15) = 210 m