Question

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

Answer 1

Answer:

12 cm

Step-by-step explanation:

Let ABCD be a parallelogram.

∴AB=17 cm,BC=11 cm and AC=26 cm

Let its diagonal AC and BD bisect each other at point O.

AO=21×AC

=21×26

=13cm

and  BO=21BD

In ΔABC, BO is a median.

∴(AB)2+(BC)2=2(BO)2+2(AO)2   (by Apollonius theorem)

(17)2+(11)2=2BO2+2(13)2

289+121=2BO2+338

2BO2=72

BO2=272=36

BO=36

=6cm

∴ length of diagonal =2×6=12 cm

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