Question

In rectangle ABCD, the angle bisector of ∠A intersects side DC at point M and the angle bisector of ∠C intersects side AB at point N. The length of CM is equal to the length of AM and it is 6 in longer than the length of DM. Find the perimeter of quadrilateral ANCM.

Answer 1

Perimeter of quadrilateral ANCM = AN+NC+CM+MA

CM=AM = x in
Therefore, AN=NC = x in
In other words, all sides of the new quadrilateral are equal.

Perimeter (P) = 4x in

Now, Cos 45 = (x-6)/x =>0.7041 = (x-6)/x => 0.7041x=x-6 =>x= 6/(1-0.70741)
x= 20.5 in

Therefore, P=4*20.5 = 82 in