Find the dimensions of rectangle RECT if the diagonals intersect at a 60 degree angle and?

Question

RC = inches. Leave your answer in simplest radical form.

rc= 18 square root of 5 inches

Answer 1

according to this info, u 've put some more points in..... intersection of diagonals is ponint D, and u'll need a point tht is a bisector of segment RE you can say ans RE is the top segment and R is on the left and mid point of RE is A

first find the necessary angles, so in
Now with this info draw an axullary line from D to midpoint
A perpendicular to RE. Now you 've a special triangle, a 30-60-90 triangle. with this you can do the following

then you can say tht RD= 9sqrt(5), and using properties of 30-60-90 triangle you can say tht DA=9sqrt(5)/2=4.5sqrt(5)
and RA=4.5sqrt(5)[sqrt(3)]=4.5sqrt(15)

now double tht will give length of RE= 9sqrt(15),

with this length of RE and RC u can now use phytogorean theroem to find EC. EC^2=RC^2-RE^2=EC^2=1620-1215,
EC^2=405

EC=TR=9sqrt(5)
RE=CT=9sqrt(15)

Answer 2

In this case l = w sqrt(3)
l^2 + w^2 = (18sqrt(5))^2
3w^2+ w^2 = 1620
4w^2 = 1620
w^2 = 405
w = sqrt(405) = sqrt(5*81) = 9 sqrt(5)
l = 9sqrt(5)*sqrt(3) = 9sqrt(15)