In a rectangle the angle between diagonals is 60°. The sum of the lengths of both diagonals and both shorter sides of the rectangle is 36 in. What are the lengths of the diagonals?

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Dragster

Mathematics

1 August, 17:44

In a rectangle the angle between diagonals is 60°. The sum of the lengths of both diagonals and both shorter sides of the rectangle is 36 in. What are the lengths of the diagonals?

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Eden Bender · Answer 1

So the diagonal and the sides of the rectangle will form a right triangle. where the the angle are 30 60 90 degrees, this is a special triangle because the shortest leg and the hypotenuse has a ratio of 1 : 2, meaning the diagonal and the shorter leg is in the same ratio. so let x be the length of the diagonal and y be the length of the shorter side.

x + y = 36

since x = 2y

2y + y = 36

3y = 36

y = 12

x = 24 in