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Question
ABCD is a rectangle. If the diagonals AC and BD intersect at O and OC = 3 cm, find BD.
ABCD is a rectangle. If the diagonals AC and BD intersect at O and OC = 3 cm, find BD.
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Solution
The correct option is D 6 cm
Given, ABCD is a rectangle and OC = 3cm.
The diagonals of a rectangle bisect each other.
So, if AC is a diagonal, intersecting BD at O, AO = OC = 3 cm.
AC = AO + OC = 3 cm + 3 cm = 6 cm.
In a rectangle, diagonals are equal.
So, AC = BD.
Since, AC = 6 cm
∴ BD = 6 cm.
Given, ABCD is a rectangle and OC = 3cm.
The diagonals of a rectangle bisect each other.
So, if AC is a diagonal, intersecting BD at O, AO = OC = 3 cm.
AC = AO + OC = 3 cm + 3 cm = 6 cm.
In a rectangle, diagonals are equal.
So, AC = BD.
Since, AC = 6 cm
∴ BD = 6 cm.
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