The adjacent sides of a parallelogram are 11cm and 17cm. If the length of one of its diagonals is 26 cm., then find the length of the other diagonal
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Answer:
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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