Question 70503: The lengths of diagonals of a rhombus are in the ratio 2:1. If the perimeter of the rhombus is 20, find the sum of the lengths of the diagonals.
I know that each side is 5. ( 20/4=5)
I know the diagonals are perpendicular to each other.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! he lengths of diagonals of a rhombus are in the ratio 2:1. If the perimeter of the rhombus is 20, find the sum of the lengths of the diagonals.
I know that each side is 5. ( 20/4=5)
I know the diagonals are perpendicular to each other.
:
Heres one way
Since the diagonals are perpendicular, there are 4 right triangles.
:
Draw a rough diagram. Label each half of the diagonals: Half the longer diagonal
= 2x, half the shorter diagonal = x.
:
One right triangle will have one side as x and the other as 2x, the hypotenuse
will = 5
:
x^2 + (2x)^2 = 5^2
:
x^2 + 4x^2 = 25
:
5x^2 = 25
x^2 = 5
x = Sqrt(5)
:
Total length of the diagonals = 6*Sqrt(5) = 13.4 units
:
did this make sense to you?
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