SOLUTION: 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

Algebra ->  Rectangles -> SOLUTION: 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      Log On


   

Question 1073300: 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?
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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Let ABCD be our rectangle and let O be the intersection point of its diagonals.

We are given that the angle (angles) AOD and BOC are of 60° each.

It implies that the triangle AOD is an equilateral triangle, as well as BOC is an equilateral triangle.


Should I continue from this point or everything is just clear to you ?


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Answer. The length of the diagonal is 12 inches.


Good luck and happy learning !