Question

if the perimeter of a square is 40cm find its length of a diagonal and it's area

Answer 1

Refer to the above attachment !!

Formula used :
Perimeter of a square = 4× Side
Area of square= side × side

And Pythagoras theorem

Answer 2

Answer:

The length of diagonals are $10\sqrt{2}$ cm and area of square is  $400$ $cm^2$.

Step-by-step explanation:

Let the side of square be $a$.

Perimeter of square = $40$ cm.

⇒ $4a = 40$ (Since perimeter of square = 4 × side)

⇒ $a=10$ cm

Thus, length of sides of square, i.e., $AB =BC =CD = AD$ = $10$ cm.

Length of diagonal, $AC = \sqrt{AD^2+CD^2}$

⇒ $AC = \sqrt{10^2+10^2}$

⇒ $AC = \sqrt{100+100}$

⇒ $AC = \sqrt{200}$

⇒ $AC = 10\sqrt{2}$ cm.

Since diagonals of square are equal.

Thus, $AC=BD=10\sqrt{2}$ cm.

Area of square = $4a^2$

                         = $4(10)^2$

                         = $4$ × $100$

                         = $400$ $cm^2$.

Thus, area of square is $400$ $cm^2$.

Therefore, length of diagonals are $10\sqrt{2}$ cm and area of square is  $400$ $cm^2$.

#SPJ3