Perimeter of quadrat inside a right angled triangle

Question

Hello,

A triangle has 90 Angle at C. The Side AC should be smaller than Side BC. The Points X,Y and Z has following properties,

a. The Point X is on side AC

b. The Point Y is on the side AB such that AX and XY are of equal lenght.

c. The Point Z is on BC such that ZYX is a right angele.

Calculate the perimeter of the quadrat CXYZ with the help of lengths of triangle ABC.

I could draw a diagram based on the information. But I am not getting hint how I should go about the perimeter of the quadrat. Appreciate any tips.

Thanx in advance.

Answer 1

based on the problem, diagram ZYXA is a parallelogram, so ZY=XA. Triangle ZYX is right angle shape. so, ZYCX is a rectangle shape. ZY=CX. now we will get conclusions CX=XA=XY=ZY=EZ, if we know any sides info: CA, CB, AB, will able to use perimeter formula to solve this problem. if we know CA, perimeter of CZYX=2CA, if we know CB, perimeter of CZYX=2CB, if we know BA, perimeter of CZYX=√2AB.