Question

ABCD is a trapezium with ABis parallel CD. The diagonals AC and BD intersect each other at O. If AO = 2x+4, OC=2x-1, DO=3 and OB = 9x-21, Find x. ​

Answer 1

$$\begin{gathered} \mathrm{ABCD}\mathrm{should}\mathrm{be}\mathrm{a}\mathrm{issosceles}\mathrm{trapezoid}. \\ \mathrm{Diagonal}\mathrm{AC}=\mathrm{AO}+\mathrm{OC}=2\mathrm{x}+4+2\mathrm{x}-1=4\mathrm{x}+3 \\ \mathrm{BD}=\mathrm{DO}+\mathrm{OB}=3+9\mathrm{x}-21=9\mathrm{x}-18 \\ \mathrm{As}\mathrm{diagonals}\mathrm{of}\mathrm{trapezium}\mathrm{are}\mathrm{equal} \\ \mathrm{so}, \\ 4\mathrm{x}+3=9\mathrm{x}-18 \\ 5\mathrm{x}=21 \\ \mathrm{x}=\frac{21}{5}\mathrm{ANS}... \end{gathered}$$