Question
Download Solution PDFThe lengths of two sides of a parallelogram are 3 cm and 10 cm. What is the sum of the squares of the diagonals of the parallelogram?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
First side of parallelogram = 3 cm
Second side of parallelogram = 10 cm
Concept used:
The sum of the squares of the diagonals of a parallelogram is equal to the sum of squares of its sides
Calculations:
Let the parallelogram be ABCD,
AB = 3 cm
BC = 10 cm
CD = 3 cm
DA = 10 cm
Using the concept,
The sum of the squares of the diagonals = (AB2 + BC2 + CD2 + DA2)
⇒ (32 + 102 + 32 + 102)
⇒ (9 + 100 + 9 + 100)
⇒ 218
∴ The sum of the squares of the diagonals of the parallelogram is 218 cm2
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