CPM Homework Help : GC Problem 7-40

In problem 7-37 you learned that the diagonals of a rhombus are perpendicular bisectors. If $ABCD$ is a rhombus with side length $15$ mm and if $BD=24$ mm, then find the length of the other diagonal, $\overline{AC}$ . Draw a diagram and show all work.

Hint:

Make an accurate and well-labeled diagram of the situation.

More help:

Use the right triangle $ΔBCE$ and the Pythagorean Theorem to solve for $x$ .

Answer:

$x=18$ mm

A, B, C, D, is a rhombus with side length 15 mm and B, D equals, 24 millimeters. Dotted lines B, D and A, C intersect in the middle at point, E. Lines B, E and E, D are both 12 millimeters. Side E, C is labeled X.