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