Question

The length of diagonal of square is 10√2 . area iwill be ? ​

Answer 1

Answer:

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The length of the diagonal of square is 10√2 . What will be it's area

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Area of the square is 100 units.

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

❥ Length of the diagonal of square = 10√2

$\Large{\underline{\underline{\bf{To FiNd:-}}}}$

❥ Area of the square.

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

Let the side of the square be a.

We know that all the sides are equal of square.

Applying Pythagoras Theorem :

★ (Hypotenuse)² = (Perpendicular)² + (Base)²

❥ (10√2)² = (a)² + (a)²

❥ 100 × 2 = a² + a²

❥ 200 = 2a²

❥ a² = $\sf\cancel\dfrac{200}{2}$

❥ a² = 100

❥ a = √100

❥ a = 10 units

We've obtained the side of square, let's find area now.

★ Area of Square = (Side)²

❥ (10)²

❥ 10 × 10

❥ 100 units.

$\mathfrak{\huge{\purple{\underline{\underline{Hence}}}}}$

Area of the square is 100 units.

Answer 2

Given :-

The length of diagonal of square is 10√2 .

To find :-

• The area of square

Formula Used :-

☯ ( Hypotenuse ) ² = ( base ) ² + ( perpendicular ) ²

Let's Begin !

• Hypotenuse = 10 √ 2
• Let the side be x

Then ,

→ ( 10 √ 2 ) ² = x ² + x ²

→ ( 10 √ 2 ) ² = 2x ²

→ 10 × 10 √ 2 × √ 2 = 2x ²

→ 100 × 2 = 2x ²

→ 200 / 2 = x ²

→ 100 = x ²

→ x = √ 100

→ x = 10 [ as per given units ]

☯ So, Area will be :-

( side ) ² = ( 10 ) ²

→ Area = 100 [ As per given units ] Ans !

Thank You !!