In the diagram, DAB = CBA = 90 degrees, EC = 5cm and ED = 10cm. The point F is the reflection of C in the line AB, and DF intersects AB at E

In the diagram, DAB = CBA = 90 degrees, EC = 5cm and ED = 10cm. The point F is the reflection of C in the line AB, and DF intersects AB at E. Given that the area of Traingle CED is 12.5 cm squared, and angle DEC =30 degrees, what is the length of CD?

read"the point F is the reflection of C in the line AB, and DF intersects AB at E."

the point F is the reflection of C in the line AB mean point F in the line AB;DF intersects AB at E mean point e is also in line AB (this is not important to this question tho)

"EC = 5cm and ED = 10cm.angle DEC =30"

CD^2=DE^2+CE^2-2DE*CE*cos(angle DEC)

CD^2=100cm^2+25cm^2-100cm*sqrt(3)/2

$${{\mathtt{CD}}}^{{\mathtt{2}}} = \left({\mathtt{125}}{\mathtt{\,-\,}}{\mathtt{50}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}\right){\mathtt{\,\times\,}}{{\mathtt{cm}}}^{{\mathtt{2}}}$$

$${\mathtt{CD}} = {\mathtt{5}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}}}{\mathtt{\,\times\,}}{\mathtt{cm}}$$  

$${\mathtt{CD}} = {\mathtt{5}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}}} \Rightarrow {\mathtt{CD}} = {\mathtt{6.196\: \!568\: \!374\: \!637\: \!379\: \!5}}$$  cm

Where's your diagram, Rodjeni?

You cannot post pics unless you are a member.   :/