Question

The diagonals of a rectangle are 12 inches and intersect at an angle of 60 degrees. Find the perimeter of the rectangle.
Answer choices:
A-48
B-12√3
C-24√3
D-12+12√3

Answer 1

If the rectangle has AB=width=w and BC=height=h, and the diagonals intersect at O, then angle BOC is 60° and is isosceles, meaning angles OBC and OCB are also 60°. That makes it an equilateral triangle, with side OB=OC = 12/2 = 6
Thus BC = 6 and AB = 6√3
P = 2(AB+BC) = 12(1+√3)