Question

The diagonal of a square is 12 cm long; find its area and length of one side.

Answer 1

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Answer 2

solution:-

• we know the all angles of square are of 90°

• all side of square are equal and diagonals are equal.

so,

let, diagonal is hypotenuse

now, by Pythagoras theorem

S = side.

=> (1st S)²+(2cd S)² =(Hypotenuse)²

=> x² + x² = (12)²

=> 2x = 12

=> x = 12/2

=> x = 6

length of sides of square are 8 cm.

=> Area of square = (side) × (side)

=> Area of square = 6 × 6

=> Area of square = 36 cm².

√=> perimeter of square = 4×(side)

√=> perimeter of square = 4 × 6

√=> perimeter of square = 24 cm

6 cm , 36 cm² and 24cm are length of side , area and perimeter of the square respectively.

i hope it helps you.