Question

In the adjoining fig. $\square$ABCD is a trapezium AB || CD and its area is 33 cm² . From the information given in the figure find the lengths of all sides of the $\square$ABCD. Fill in the empty boxes to get the solution.

Answer 1

$\square$ABCD is a trapezium.
AB || CD
A($\square$ABCD) = $\frac{1}{2}\left(\mathrm{AB}+\mathrm{CD}\right)\times \boxed{\mathrm{AM}}$
$$\begin{gathered} 33=\frac{1}{2}\left(x+2x+1\right)\times \boxed{\left(x-4\right)} \\ \therefore \boxed{33\times 2}=\left(3x+1\right)\times \boxed{\left(x-4\right)} \\ \therefore 3x^2+\boxed{11x}-\boxed{70}=0 \\ \therefore 3x\left(x-7\right)+10\left(x-7\right)=0 \\ \therefore \left(3x+10\right)\left(x-7\right)=0 \\ \therefore \left(3x+10\right)=0\mathrm{or}\boxed{x-7}=0 \\ \therefore x=\frac{-10}{3}\mathrm{or}x=\boxed{7} \end{gathered}$$
But length is never negative.
$\therefore x\ne \frac{-10}{3}\therefore x=\boxed{7}$
AB = 7, CD = 15, BC = 5