2
Question
Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm, then find BO and if ∠CAD = 35°, then find ∠ACB.
(2 marks)
(2 marks)
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Solution
i) AC = 8 cm …(i) [Given]
□ABCD is a rectangle [Given]
∴ BD = AC [Diagonals of a rectangle are congruent]
∴ BD = 8 cm
(1 mark)
BO = 12 BD [Diagonals of a rectangle bisect each other]
∴ BO = 12 × 8
∴ BO = 4 cm
(1 mark)
□ABCD is a rectangle [Given]
∴ BD = AC [Diagonals of a rectangle are congruent]
∴ BD = 8 cm
(1 mark)
BO = 12 BD [Diagonals of a rectangle bisect each other]
∴ BO = 12 × 8
∴ BO = 4 cm
(1 mark)
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