Question

Find the area and the perimeter of a square with diagonal 24 cm. [Take V2 = 1.411.

Answer 1

Answer:

Area = 288cm²; Perimeter = 276.566 cm

Step-by-step explanation:

If the diagonal of a square is "s", then its side is s/√2

Therefore:

Side of given square with diagonal 24cm = s = (24/√2) cm

Area of square = s² = (24/√2)² cm² = (24*24)/2 cm² = 12*24cm² = 288cm²

Perimeter of square = 4s = 4*(24/√2) cm = 2*(√2)²*96/√2 cm

                                          = 2*√2*96 cm

                                          = 192*√2 cm

                                           = 276.566 cm (Using √2 = 1.411)

More explanation:

The triangle formed by the diagonal and two adjacent sides of a square is an isoceles right triangle with sides "s" and "s". Using Pythagoras' theorem, the length of the diagonal works out to s√2.

diagonal² = s² + s²

                 = 2s²

Thus,

diagonal = √(2s²) = s√2

Hence, if the length of the diagonal is "x", then the side = x/√2