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

Explanation:

Step1: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So \(AE = EC\).
Set up the equation \(3y + 6=2y + 4\).

Step2: Solve for \(y\)

Subtract \(2y\) from both sides: \(3y-2y+6 = 2y-2y + 4\), which gives \(y+6=4\).
Subtract \(6\) from both sides: \(y=4 - 6=- 2\). (This is wrong, we should use \(AE = EC\) is wrong, actually in parallelogram \(DE=EB\) (diagonals bisect each other). So \(3y + 6=5y-10\).
Subtract \(3y\) from both sides: \(6=2y-10\).
Add \(10\) to both sides: \(16 = 2y\).
Divide both sides by \(2\): \(y = 8\).

Step3: Find the length of \(BD\)

Since \(BD=2\times EB\), and \(EB=(5y - 10)\) cm. Substitute \(y = 8\) into \(EB\): \(EB=5\times8-10=40 - 10=30\) cm.
Then \(BD = 2\times30=60\) cm.

Answer:

\(60\) cm