Question

what is the length of segment eb in parallelogram abcd? 30 units 34.5 units 69 units 138 units

Explanation:

Step1: Use parallelogram property

In a parallelogram, the diagonals bisect each other. So, $AE = EC$ and $DE=EB$. Here, we have $2x + 9=3x - 21$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $9=x - 21$. Then add 21 to both sides: $x=9 + 21=30$.

Step3: Find length of $EB$

Substitute $x = 30$ into the expression for $EB$ (which is $3x-21$). So, $EB=3\times30 - 21=90 - 21 = 69$.

Answer:

69 units