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Question
Choose the correct alternative:
The diagonal of a square is `10sqrt(2)` cm then its perimeter is ______
Options
10 cm
`40 sqrt(2)` cm
20 cm
40 cm
Solution
40 cm
In ∆ABC,
∠B = 90°, and ∠BAC = ∠BCA = 45°
∴ `"AB" = 1/sqrt2 "AC"` ...[Theorem of 45° – 45° – 90° triangle]
∴ `"AB" = 1/sqrt2 xx 10sqrt2`
∴ AB = 10 cm
∴ Perimeter of square= 4 (AB) = 4 × 10 = 40 cm.
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