SOLUTION: One diagonal of a rhombus has the same length, 10cm, as each side. How long is the other diagonal

Question 523748: One diagonal of a rhombus has the same length, 10cm, as each side. How long is the other diagonal
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
One diagonal of a rhombus has the same length, 10cm, as each side. How long is the other diagonal

Then it it is two equilateral triangles with a common side, like this,
where all the black line segments are 10 cm each:

We want to know the length of the green line segment:
So we look at just one half of the top which is this:

The bottom side is 5cm because the diagonals of a parallelogram bisect
each other (and a rhombus is a parallelogram). The hypotenuse is a side
of the rhombus, so it is 10cm, so the green line in that triangle is
found by the Pythagorean theorem:
c� = a� + b�
10� = 5� + b�
100 = 25 + b�
75 = b�
= b
= b
5 = b
So the entire diagonal is twice that or
10 or about 17.32cm
Edwin

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