Final answer:
By setting up the perimeter equation for the parallelogram ABCD, solving for x, and then substituting back into the equation, we find that the value of y is 5.
Step-by-step explanation:
To find the value of y for the parallelogram ABCD with a given perimeter of 80, we can sum up the lengths of all its sides and set that equal to the perimeter. Since opposite sides of a parallelogram are equal, we have: AB = CD and AD = BC. Given that AB = x + 16, CD = 2x + 8, and AD (also BC) = 4y - 4, we can write the perimeter equation as:
2(AB) + 2(AD) = Perimeter
2(x + 16) + 2(4y - 4) = 80
Expanding this, we get:
2x + 32 + 8y - 8 = 80
Subtract 32 from both sides and add 8 to both sides we get:
2x + 8y = 56
Since AB is equal to CD, we can also write:
x + 16 = 2x + 8
Subtract x from both sides to find x:
16 = x + 8
x = 8
Plug x back into the perimeter equation:
2(8) + 8y = 56
16 + 8y = 56
Subtract 16 from both sides to isolate 8y:
8y = 40
Divide both sides by 8 to solve for y:
y = 5
Therefore, the value of y is 5.