Question

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 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

Answer 2

The length of the diagonals are 12 inches

Properties of a rectangle:

• The length of the two diagonal are equal
• Opposite sides are equal
• Diagonals are of equal length
• Diagonal are bisector of each other

Therefore, the angle where the diagonal intersect are 60 degrees each. Therefore,

AOB = 60 degrees

DOC = 60 degrees

where

O is the centre where they intersect

The triangles are equilateral triangles. Therefore, the sides length are the same.

shorter sides  = 2x

Length of the two diagonal = 2x + 2x  = 4x

Therefore,

2x + 4x = 36

6x = 36

x = 36 / 6

x = 6

The length of the diagonals are 2(x) = 2(6) = 12 inches

learn more on rectangle here: https://brainly.com/question/10690825