Question

Find the side and perimeter of a square whose diagonal is 10 cm.

Answer 1

Let ABCD be the given square.

AC = 10 cm

Let the side of the square be x cm.

∴ AB = BC = x cm

In Δ ABC,

∠ABC = 90°   ...(Angle of a square)

∴ by Pythagoras theorem,

AC² = AB² + BC²

∴ 10² = x² + x²

∴ 100 = 2x²

∴ x² = `100/2`

∴ x² = 50

∴ x = `5sqrt2`

∴ AB = `5sqrt2` cm

∴ side of a square is `5sqrt2` cm.

Perimeter of a square = 4 × side

= 4 × `5sqrt2`

= `20sqrt2` cm

∴ Side of a square is `5sqrt2` cm and its perimeter is `20sqrt2` cm.