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

Answer:

The length of the diagonal AC=20 cm.

Step-by-step explanation:

From ΔOBP and ΔABC, we have

$\frac{OB}{AB}=\frac{BP}{BC}$( O and P are mid points)

∠B=∠B(Common)

Therefore, by SAS rule,

ΔOBP is similar toΔABC

Thus, $\frac{OB}{AB}=\frac{OB}{2OB}=\frac{1}{2}$

⇒$\frac{OP}{AC}=\frac{1}{2}$

⇒$AC=2{\times}OP$

⇒$AC=2{\times}10$

⇒$AC=20 cm$

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