Question

the perimeter of a square is 16 cm find the length of its diagonals​

Answer 1

Answer:

4√2

Step-by-step explanation:

perimeter = 16cm

perimeter of square = 4a

                        16      = 4a

                          4      = a

therefore side = 4cm

since all angles of square are 90°

by pythagoras theorem

 dia^2 = a^2 + a^2

           =  4^2 + 4^2

           = 16 +16

           = 32

dia = √32 = 4√2

hope this helps you dear..

Answer 2

Answer:

4√2 cm or 5.656 cm

Step-by-step explanation:

We know that the perimeter of a square is 4s where s is the length of the side

4s = 16cm

s = 16/4 = 4cm

Now we know that a square has two right Triangles

so, a² + b² = c²

s² + s² = d² where s is the side length and d is the diagonal

2s² = d²

d = √2s²

d = √2 × 4 × 4 = 4√2 cm

So the length of the diagonal = 4√2 cm

OR

also, √2 is approximately 1.414

if you want the full value then

4 × √2 = 4 × 1.414 = 5.656 cm

Hope you understood it........All the best