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Question
The diagonal of a square is `10sqrt(2)` cm then its perimeter is ______.
Options
10 cm
`40 sqrt(2)` cm
20 cm
40 cm
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Solution
40 cm
Explanation:
In ∆ABC,
∠B = 90° and ∠BAC = ∠BCA = 45°
∴ `AB = 1/sqrt(2) AC` ...[Theorem of 45° – 45° – 90° triangle]
∴ `AB = 1/sqrt(2) xx 10sqrt(2)`
∴ AB = 10 cm
∴ Perimeter of square = 4 (AB) = 4 × 10 = 40 cm.
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