Question

find the diagonal of a square whoes side is 10​

Answer 1

Answer:

the length of diagonal would be 10√2.

Step-by-step explanation:

a square has right angles on all sides. imagining as a right angled triangle and apply Pythagoras theorem you will get your answer.

Answer 2

Answer :

Diagonal , d = 10√2 or 1.414 units

Solution :

• Given : Side , a = 10 units
• To find : Diagonal , d = ?

We know that ,

The length of diagonal of a square of side a is given as ;

=> d = √2a

=> d = √2×10

=> d = 10√2

OR

=> d = 10×1.414

=> d = 14.14 units

Hence ,

Diagonal of the square is 10√2 or 14.14 units .

**************************************************

To find an expression for the diagonal d of a square of side a :

• Take a square ABCD .

• Draw the diagonal AC .

• Clearly , the ∆ABC is a right angled at vertex B .

• Now , applying Pythagoras theorem in right ∆ABC , we have ;

=> AC² = AB² + BC²

=> d² = a² + a²

=> d² = 2a²

=> d = √(2a²)

=> d = √2a

Hence ,

The diagonal d of the square of side a is given as ; d = √2a .