Question

4. DECK is a parallelogram. Find the values of x and y.

Answer 1

Answer:

The value of  x  = 5 and y = 2.

Step-by-step explanation:

Here, given DECK is a parallelogram.

Also, KT = 2x + y  , DT = x + 2y  , TE = 12   and TC = 9

Now, in parallelogram:

DIAGONALS IN A PARALLELOGRAM BISECT EACH OTHER

Also, in the parallelogram DECK,

Sides DC and KE are two diagonals.

⇒ T is the mid point of AC and KE.

⇒ KT = TE and DT = TC ( as diagonals are bisected)

⇒  2 x +   y =  12 and x  +  2y = 9

So here, the set of two equations are:

2 x +   y = 12  ....... (1)

x  +  2 y = 9  ....... (2)

Multiply (2) with -2 and add with (1), we get:

2 x +  y  - 2 x - 4 y = 12  - 18

or, - 3 y = - 6

or, y = 2

If y = 2, then x  +  2 (2) = 9 or, x  = 5

Hence the values of  x  = 5, y = 2