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?

Question

Mathematics

Dennis Chung

13 June, 15:57

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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Angelo · 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