Question

if the length of diagonal of square is 16 cm find it's perimeter​

Answer 1

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Given that the diagonal of a square is 16cm .

Now we know that,

• All sides of a square are equal .
• And all angles of a square is 90° .

Now let us take the side of square be a .

So , in the right Angled triangle formed ,

➳ hypontenuse ² = base² + perpendicular ².

➳ (16cm)² = a² + a².

➳ 256cm² = 2a².

➳ a² = 256cm²/2.

➳ a² = 128cm².

➳ a = √ 2⁷ cm².

➳ a = 2³ × √2cm.

➳ a = 8√2 cm.

Now , we know that the perimeter of square is ,

★ Perimeter ( square) = 4 (side) ★

➳ Perimeter = 4(side).

➳ Perimeter = 4 × 8√2cm.

➳ Perimeter = 32√2 cm.

Hence the perimeter of square is 32√2cm.