# SOLUTION: 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

Algebra ->  Algebra  -> Pythagorean-theorem -> SOLUTION: 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      Log On

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 Click here to see ALL problems on Pythagorean-theorem 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(15647)   (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?