Dimensions of Rectangle when Value of Diagonal is Given

Topic : Dimension of Rectangle

Question : Find the dimensions of rectangle RECT if the diagonals intersect at a 60º angle and RC = 18√5 inches. Leave your answer in simplest radical form.

Solution :

Given RC = 18√5 inches

Since RECT is a rectangle both diagonals are equal and bisect eachother

we have OE = OC = OT = OR = 1/2(18√5) = 9√5inches

Consider triangle OEC as
∟EOC = 60º and OE = OC

It is an equilateral triangle. Hence EC = OE = OC = 9√5

To find TC :

Consider triangle OCT; using sine rule

9√5 / Sin 30º = TC / Sin 120º

TC = (Sin 120º * 9√5 ) / Sin 30º

= [(√3/2) * 9√5] /1/2

= 9√5 * √3

= 9√15 inches

So the sides TC = RE = 9√15 inches

Hence the dimensions of RECT are 9√15 inches , 9√5 inches