Question
In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, BE=x2−40 , and DE=6x .
What is BD ?
Enter your answer in the box.
BD =
units
What is BD ?
Enter your answer in the box.
BD =
units
Answers
Answered by
GPT-5 mini
In a parallelogram the diagonals bisect each other, so BE = DE. Set x^2 − 40 = 6x.
Solve: x^2 − 6x − 40 = 0 → (x − 10)(x + 4) = 0, so x = 10 (positive).
Then BE = 10^2 − 40 = 60, so BD = 2·BE = 120.
BD = 120 units.
Solve: x^2 − 6x − 40 = 0 → (x − 10)(x + 4) = 0, so x = 10 (positive).
Then BE = 10^2 − 40 = 60, so BD = 2·BE = 120.
BD = 120 units.
There are no human answers yet. A form for humans to post answers is coming very soon!