Question

# If ABCD is a rhombus, AC is itssmaller diagonal and ∠ ABC=60∘,then find the length of a side of the rhombus when AC=7 cm.

A
6 cm
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B
6.5 cm
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C
7 cm
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D
7.5 cm
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Solution

## The correct option is C 7 cmGiven: ∠ ABC=60∘ and AC = 7 cm In rhombus ABCD, AB=BC(In a rhombus all sides are equal.) ∴△ABC is isosceles and base anglesare equal. Given: ∠ABC=60o ∵Rhombus is a parallelogram and in a parallelogram, the adjacent angles are supplementary. ⇒∠ABC+∠BCD=180∘⇒60∘+∠BCD=180∘⇒∠BCD=180o−60o⇒∠BCD=120o ∵Diagonals in rhombus bisect the angles. ∴∠BCA=∠CAB=120∘2=60∘ ∴△ ABC is an equilateral triangle. So, AC = AB = BC = 7 cmTherefore, length of a side of the rhombus is 7 cm.

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