Question

lauren 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 60 cm 16 cm 30 cm 8 cm

Explanation:

Step1: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So, \(DE = BE\) and \(AE=CE\). We can use \(AE = CE\) to find the value of \(y\).
Set \(3y + 6=2y + 4\).
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 \(DE=BE\) instead.

Set \(3y + 6=5y-10\).
Subtract \(3y\) from both sides: \(3y-3y + 6=5y-3y-10\), so \(6 = 2y-10\).
Add \(10\) to both sides: \(6 + 10=2y-10 + 10\), \(16=2y\).
Divide both sides by \(2\): \(y = 8\).

Step2: Calculate the length of \(BD\)

Since \(BD=2\times BE\) (diagonals bisect each other in a parallelogram), and \(BE=(5y - 10)\) cm.
Substitute \(y = 8\) into \(BE\): \(BE=5\times8-10=40 - 10=30\) cm.
Then \(BD = 2\times30=60\) cm.

Answer:

\(60\) cm