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
