In trapezium ABCD, AB = 21 cm, CD = (6x - 1) cm and AB ∥ CD. If X and Y are the mid points of the diagonal AC and BD, respectively and XY = (2x + 1) cm. Then, find is the value of x. (If AB > CD)

Question

Question

Answer 1

F1 M.S 15.5.20 Pallavi D37

We know that, if X and Y are the mid-points of diagonal AC and BD, respectively of trapezium ABCD,

\(XY = \frac{{AB - CD}}{2}\)

\(\Rightarrow \;\left( {2x + 1} \right) = \frac{{21 - \left( {6x - 1} \right)}}{2}\)

⇒ 2(2x + 1) = (21 - 6x + 1)

⇒ 4x + 2 = 22 - 6x

⇒ 4x + 6x = 22 - 2

⇒ 10x = 20

⇒ x = 2