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Choose the correct alternative: The diagonal of a square is 1012 cm then its perimeter is - Geometry

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MCQ
Fill in the Blanks

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

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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.

Concept: Property of 30°- 60°- 90° Triangle Theorem
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