SOLUTION: the diagonals of a rectangles are 24 inches long intersect at an angle of 60 degrees.find the perimeter of the rectangle?

Question 498197: the diagonals of a rectangles are 24 inches long intersect at an angle of 60 degrees.find the perimeter of the rectangle?
Answer by cleomenius(959) (Show Source): You can put this solution on YOUR website!
Without a diagram, I am going to assume that the diagonals create two 60 degree angles on the left and right of where they cross.
Being a rectangle, the diagonals are congruent, so the bisected diagonals will be congruent also.
This will form a triangle from the two bisected segment of the diagonal against one side of the width they connect to.
The angles of the newly formed triangle will be congruent at the side against the width, since they are congruent to opposite sides.
So we have the angle given as 60 degrees, the total is 180 degrees. 180 - 60 = 120 degrees, which divided by 2 gives us equal angles of 60 degrees.
This is an equilateral triangle with all angles equal to 60 degrees, so all the sides will be equal.
The width therefore is 1/2 the diagonal, or 12 inches.
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We know the width and the diagonal, this can now be treated as a right traingle with one leg of 12 and a hypotenuse of 24.
12^2 + length^2 = 24^2
144 + b^2 = 576
576 = 144 = 432
= Approx 20.8 inches.
Cleomenius

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