Question

lourdes is making a frame in the shape of a parallelogram. she adds diagonal braces to strengthen the frame.
how long is the brace that connects points b and d?
○ 8 cm
○ 16 cm
○ 30 cm
○ 60 cm
line segments are marked as: (3y + 6) cm, (5y - 10) cm, (2y + 4) cm

Explanation:

Step1: Use parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $AE = CE$.
$3y + 6 = 2y + 4$

Step2: Solve for y

Subtract $2y$ and 6 from both sides:
$3y - 2y = 4 - 6$
$y = -2$
Note: Using the other pair of bisected segments $BE = DE$ confirms this: $5y - 10 = 3y + 6$ → $2y = 16$ → $y=8$. This is the valid solution (negative length is impossible), so we use $y=8$.

Step3: Calculate length of BE

Substitute $y=8$ into $BE = 5y - 10$:
$BE = 5(8) - 10 = 40 - 10 = 30$ cm

Step4: Calculate length of BD

Since $BD = BE + DE$ and $BE=DE$, $BD = 2 \times BE$
$BD = 2 \times 30 = 60$ cm

Answer:

60 cm