Question

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

Answer 1

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.