Question

The length of the line segment joining the midpoints of sides AB and BC of the parallelogram ABCD is 10. Find the length of diagnol AC

Answer 1

The length of the diagonal AC=20 cm.

Explanation:

From ΔOBP and ΔABC, we have

`(OB)/(AB)=(BP)/(BC)`( O and P are mid points)

∠B=∠B(Common)

Therefore, by SAS rule,

ΔOBP is similar toΔABC

Thus,
`(OB)/(AB)=(OB)/(2OB)=(1)/(2)`

⇒
`(OP)/(AC)=(1)/(2)`

⇒
`AC=2{*}OP`

⇒
`AC=2{*}10`

⇒
`AC=20 cm`

Thus, the length of the diagonal AC=20 cm.