SOLUTION: ABCD IS A RHOMBUS, AC=10CM AND AB=12CM. FIND BD.

Question 698535: ABCD IS A RHOMBUS, AC=10CM AND AB=12CM. FIND BD.

Found 2 solutions by Simnepi, neatmath:
Answer by Simnepi(216) (Show Source): You can put this solution on YOUR website!
since the angles of a rhombus bisect each other and are perpendicular and meet at E you can make right angled triangle ABE
AB=12cm, AE=5cm and BE is half BD
Using Pythagoras
AE^2 + BE^2 = AB^2
5^2 + BE^2 = 12^2
25 + BE^2 = 144
BE^2 = 144 - 25
BE^2 = 119
BE =
BE = 10.9cm (to 1 decimal place)
BD = 21.8cm
Answer by neatmath(302) (Show Source): You can put this solution on YOUR website!

A rhombus is a parallelogram with 4 equal sides.

So if you know the length of one side, you know the length of all 4 sides.

Also, the diagonals of a rhombus always bisect each other,

and they are always perpendicular to each other.

So let's draw the diagonals, where M is the intersection of the diagonals,

and notice we will form a right triangle AMD.

Using this, we can find DM, and we know that

We can use the Pythagorean Theorem at this point.

Since , we can see that:

So diagonal cm or approximately 21.8 cm.

I hope this helps! Keep practicing! :)

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