in the parallelogram shown, ae = t + 2, ce = 3t - 14, and de = 2t + 8. what is the length of line segment…
in the parallelogram shown, ae = t + 2, ce = 3t - 14, and de = 2t + 8. what is the length of line segment db? 20 units 24 units 48 units 68 units
Answer
Explanation:
Step1: Use parallelogram property
In a parallelogram, the diagonals bisect each other. So $AE = CE$. $t + 2=3t - 14$
Step2: Solve for t
Subtract t from both sides: $2 = 2t-14$. Add 14 to both sides: $16 = 2t$. Divide both sides by 2: $t = 8$.
Step3: Find length of DE
Substitute $t = 8$ into the expression for $DE$. $DE=2t + 8=2\times8 + 8=16 + 8=24$.
Step4: Find length of DB
Since the diagonals bisect each other, $DB = 2DE$. $DB=2\times24 = 48$.
Answer:
48 units