Trapezium diagonals

It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC.

Correct result:

x =  10 cm

Solution:

$$\begin{gathered} a=12\text{ cm } \\ c=8\text{ cm } \\ {f}_1=6\text{ cm } \\ {f}_1:a=f_2:c \\ {f}_2=f_1\cdot {\displaystyle \frac{c}{a}}=6\cdot {\displaystyle \frac{8}{12}}=4\text{ cm } \\ x=f_1+f_2=6+4=10\text{ cm} \end{gathered}$$

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