Parallelogram RECT is a rectangle. If EC = x + y, RT = 2x - y, RE = 2x + y, and TC = 3x - 3, what are the values of the variable

The values of the variable are 3 and 6.

Step-by-step explanation:

In parallelogram RECT is a rectangle,

EC = x + y, RT = 2x - y, RE = 2x + y and TC = 3x - 3

To find, the values of the variable = ?

∵ The opposite sides are equal.

∴ RE = TC and RT = EC

2x + y = 3x - 3

⇒ x - y = 3 ... (1)

Also,

2x - y = x + y

⇒ x - 2y = 0 ... (2)

Subtracting (1) from (2), we get

∴ x - y - (x - 2y) = 3 - 0

⇒ x - y - x + 2y = 3

⇒ y = 3

Put y = 3 in equation (1), we get

x - 3 = 3

⇒ x = 3 + 3 = 6

∴ x = 6 and y = 3

Thus, the values of the variable are 3 and 6.