Solve any three sub-questions:

Adjacent sides of a parallelogram are 11 cm and 17 cm. If the length of one of its diagonal is 26 cm, find the length of the other.

The figure is as follows:

Therefore the figure ABCD is the required parallelogram.

AB = 11 cm

BC = 17 cm

Diagonal AC = 26 cm

In a parallelogram the diagonals bisect each other,

∴ O is the midpoint of AC and BD

∴ AO = 1/2 AC

= 1/2 × 26

∴ AO = 13 cm.

In ∆ADB, segment AO is the median.

Apollonius’s Principle can be applied to this problem

Statement of the Theorem: If O be the mid-point of the side MN of the triangle LMN, then LM � + LN � = 2(LO � + MO �).

By Apollonius’s Principle,

AB² + AD² = 2AO² + 2BO²

17² + 11² = 2× 13² + 2BO²

289 + 121 = 2 × 169 + 2BO²

410 = 338 + 2BO²

2BO² = 410 -338

2BO² = 72

BO² = 36

BO = 6 cm.

∴ Length of Diagonal BD = 2 × BO

∴ BD = 12 cm.