Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find y.
We can start by using the property of diagonals in a parallelogram:
In a parallelogram, the diagonals bisect each other. This means that AE = CE and BE = DE.
From the given information, we have:
AE = 2x
BE = y + 10
CE = x + 2
DE = 4y - 8
Since AE = CE, we can write:
2x = x + 2
Simplifying this equation, we get:
2x - x = 2
x = 2
Now, let's use the fact that BE = DE:
y + 10 = 4y - 8
Simplifying this equation, we get:
10 + 8 = 4y - y
18 = 3y
Dividing both sides by 3, we get:
y = 18/3
y = 6
Therefore, the value of y is 6.
To find the value of y, we can use the fact that the diagonals of a parallelogram bisect each other. This means that AE is equal to CE, and BE is equal to DE.
Since AE = 2x and CE = x + 2, we can set up the following equation:
2x = x + 2
By subtracting x from both sides of the equation, we have:
x = 2
Now we can substitute the value of x into the equation for BE and DE:
BE = y + 10 and DE = 4y - 8
Since BE = DE, we can set up the following equation:
y + 10 = 4y - 8
By subtracting y from both sides of the equation, we have:
10 = 3y - 8
By adding 8 to both sides of the equation, we have:
18 = 3y
Finally, divide both sides of the equation by 3 to isolate y:
y = 6
Therefore, the value of y is 6.
since the diagonals bisect each other,
2x = x+2
y+10 = 4y-8