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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?