In the figure PQRS is a trapezium with PQ parallel to SR.
The diagonal of the trapezium meet at X.
U lies on SP and T lies on RQ such that UT is a line segment through X parallel to PQ.
The length of PQ is 12 cm and the length of SR is 3 cm.
What, in centimetres, is the length of UT?
I tried to use the Thales theorem but I did not get a solution. I read a lot of about properties of trapezium but I couldn't find any useful information. So I need some guidance. Which property or theorem can be used for this question.
$$\frac{UX}{12}=\frac{SX}{SQ}=\frac{1}{1+\frac{XQ}{SX}}=\frac{1}{1+\frac{12}{3}}=\frac{1}{5}.$$ Thus, $$UX=2.4.$$ By the same way we can get $$TX=2.4,$$ which gives the answer: $$UT=2\cdot2.4=4.8.$$