SOLUTION: The perimeter of a rhombus is 40 cm, and one diagonal is 12 cm long. How long is the other diagonal? This question was already answered, but I don't understand the solution pos

Algebra ->  Triangles -> SOLUTION: The perimeter of a rhombus is 40 cm, and one diagonal is 12 cm long. How long is the other diagonal? This question was already answered, but I don't understand the solution pos      Log On


   

Question 717056: The perimeter of a rhombus is 40 cm, and one diagonal is 12 cm long. How long is the other diagonal?
This question was already answered, but I don't understand the solution posted. Please help me!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
All 4 sides in a rhombus have the same length s and that makes the perimeter 4s
4s=40cm --> s=10cm
The diagonals split the rhombus into 4 congruent triangles, like this:
In the right triangle with the colorful side measurements marked, the vertical leg (red) is half of the 12 cm diagonal, so it measures 6 cm.
The hypotenuse is the blue side of the rhombus, measuring 10 cm.
The horizontal leg (green) measures x cm, and is half of the (green) horizontal diagonal.
According to the Pythagorean theorem about right triangles,
x%5E2%2B8%5E2=10%5E2 --> x%5E2%2B64=100 --> x%5E2=100-64 --> x%5E2=36 --> x=6
The length of the other (green) diagonal is 2%2Ax=2%2A6cm=highlight%2812cm%29