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

Answer 1

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.