Question

if diagonal of a square is 13 cm find its side Given (1) PQRS is a square​

Answer 1

Answer:

13$\sqrt{2\\}$/2

Step-by-step explanation:

diagonal of square = side$\sqrt{2}$

13 = side$\sqrt{2}$

13/$\sqrt{2}$ = side

on rationalising:-

13*$\sqrt{2}$/$\sqrt{2}$*$\sqrt{2}$ = side

13$\sqrt{2\\}$/2 = side.

Answer 2

To Find:-

• The side of square PQRS

Step-by-step explanation:

Given that,

• The diagonal of square = 13cm
• PQRS is a square.

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Method 1 :-

• Finding the side of square by applying pythagoras theorem :-

We have,

• PQRS as the square.

∴ PQ, QR, RS and SP are the sides.

Assumption:

• Let us assume the sides of square as (x).

We know,

All angles of square measures 90°.

Therefore,

• PQ² + QR² = PR² ... Pythagoras theorem

⟶ PQ² + QR² = PR²

⟶ x² + x² = PR²

⟶ 2x² = PR²

⟶ 2x² = 13²

⟶ 2x² = 169

⟶ x² = 169/2

⟶ x = √(169/2)

⟶ x = 13/√2

⟶ x = 9.19

Hence, The side of square is 9.19cm.

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Method 2 :-

• Finding the side of square by putting the formula of diagonal of square :-

We know,

Diagonal of square = a√2 units,

Where,

• a = side of square.

⟶ a√2 = 13

⟶ a = 13/√2

⟶ a = 9.19

Hence, The side of square is 9.19cm.

Required Answer :-

• The side of square is 9.19cm.