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

Explanation:

Step1: Use parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $DE = BE$.
$3y + 6 = 5y - 10$

Step2: Solve for y

Rearrange to isolate y:
$6 + 10 = 5y - 3y$
$16 = 2y$
$y = \frac{16}{2} = 8$

Step3: Calculate length of DE

Substitute $y=8$ into $DE = 3y + 6$:
$DE = 3(8) + 6 = 24 + 6 = 30$

Step4: Find length of BD

Since $BD = DE + BE$, and $DE=BE=30$:
$BD = 30 + 30 = 60$

Answer:

60 cm