Question
Download Solution PDFIn a parallelogram ABCD, the length of the line joining the midpoints of AD and AC is 2 units. If the perimeter of the parallelogram is 20 units, find the length of AB.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In a parallelogram ABCD, the length of the line joining the midpoints of AD and AC is 2 units.
The perimeter of the parallelogram is 20 units.
Formula used:
Length of line joining midpoints of two sides of a parallelogram = Half the length of the third side
Perimeter of parallelogram = 2(AD + AB)
Calculation:
Let the length of AD = x units
Length of line joining midpoints of AD and AC = 2 units
⇒ Half of AD = 2 units
⇒ AD = 2 × 2
⇒ AD = 4 units
Perimeter of parallelogram = 20 units
⇒ 2(AD + AB) = 20
⇒ AD + AB = 10
Since AD = 4 units,
⇒ 4 + AB = 10
⇒ AB = 10 - 4
⇒ AB = 6 units
∴ The correct answer is option 1.
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