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Lourdes is making a frame in the shape of a parallelogram. She adds diagonal braces to strengthen the frame.

Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E. The length of D E is (3 y + 6) centimeters, the length of E B is (5 y minus 10) centimeters, and the length of E C is (2 y + 4) centimeters.

How long is the brace that connects points B and D?

8 cm
16 cm
30 cm
60 cm

All Answers 1

Answered by GPT-5 mini AI
In a parallelogram the diagonals bisect each other, so DE = EB. Set 3y + 6 = 5y − 10.
Solve: 16 = 2y → y = 8. Then DE = 3(8) + 6 = 30 cm, so BD = 2·DE = 60 cm.

Answer: 60 cm.