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? (5y - 10) cm (3y + 6) cm (2y + 4) cm 8 cm 16 cm 30 cm 60 cm

Explanation:

Step1: Use property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So, $AE = EC$ and $DE=EB$. We can set up an equation using the expressions for the segments of one of the diagonals. Let's use the fact that $AE = EC$. So, $3y + 6=2y + 4$.

Step2: Solve the equation for y

Subtract $2y$ from both sides: $3y-2y+6=2y - 2y+4$, which simplifies to $y+6 = 4$. Then subtract 6 from both sides: $y=4 - 6=-2$. This is incorrect. Let's use $DE = EB$. So, $5y-10=3y + 6$.

Step3: Solve the new - equation for y

Subtract $3y$ from both sides: $5y-3y-10=3y-3y + 6$, which gives $2y-10 = 6$. Add 10 to both sides: $2y=6 + 10=16$. Divide both sides by 2: $y=\frac{16}{2}=8$.

Step4: Find the length of BD

The length of $BD=2\times(5y - 10)$ (since $BD = 2EB$). Substitute $y = 8$ into the expression for $EB$ (where $EB=5y - 10$). First, $EB=5\times8-10=40 - 10=30$. Then $BD = 2\times30=60$ cm.

Answer:

60 cm