Question

(i)
One of the adjecent sides of a parallelogram is 11 cm and the other is 17 cm. If one
of the diagonals is 26 cm. Find the other diagonal.
​

Answer 1

Answer: 12 cm

Step-by-step explanation:

Use the diagram attached

DB = 26 cm

So, DO = 13 cm

DO = OB = 13 cm

 

Using Apollonius Theorem

AD²+ AB² = 2AO² + 2DO²

11² + 17² = 2AO² + 2(13)²

121 + 209 = 2AO² + 2(169)

410 = 2AO² + 338

2AO² = 410 – 338

2OA² = 72

OA²= 36

OA  = 6

AC = 2OA = 2X6 = 12

∴The length of the other diagonal = 12 cm.

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