Question

A square has diagonals of length 10 cm. Find the sides of the square.​

Answer 1

Answer :-

◍ The side of the square is 5√2 cm.

Given :-

✧ Length of the diagonal = 10cm

To find :-

・The side of the square

Concept Using :-

Pythagoras Theorem,

→ In a right angled triangle the square of hypotenuse is equal to the sum of square of base and perpendicular.

$\star \boxed{\tt{ {(Hypothenuse)}^{2}= {(Base)}^{2} + {(Perpendicular)}^{2}}}$

Solution :-

Diagram of the solution is in the attachment.

In the diagram,

AB = Side of the square = S

AC = Diagonals of the square = Hypothenuse

As, we know that all sides of a square are equal. Therefore, BC = AB = S

→ In right angled ∆ABC,

Using Pythagoras Theorem,

=> (AC)² = (AB)² + (BC)²

=> (10cm)² = (S)² + (S)²

=> 100cm² = S² + S²

=> 100cm² = 2S²

$\tt{=> \dfrac{100 {cm}^{2} }{2} = {S}^{2} } \\ \\ \tt{ = > 50 {cm}^{2} ={S}^{2} } \\ \\ \tt{ = >\sqrt{50 {cm}^{2}} = S } \\ \\ \tt{ = > 5 \sqrt{2}cm } = S$

The length of the side = 5√2 cm

More Information :-

◍ Perimeter of the square = 4 × square

◍ Area of the rectangle = Length × Breadth

◍ Perimeter of the rectangle = 2(Length + Breadth)

◍ Area of circle = π × (radius)²

◍ Circumference of the circle = 2 × π × radius

Answer 2

Answer:

Question⤵

➡A square has diagonals of length 10 cm. Find the sides of the square.

Answer⤵

➡The side of square is 5√2.

Given⤵

➡Length of diagonal =10cm.

To find ⤵

➡The side of the square.

Concept using ⤵

➡Pythagoras theorem,

In a right angled triangle the square of hypotenuse is equal to the sum of the square of base and perpendicular.

Hypotenuse²=Base²+Perpendicular²

Solution⤵

In the diagram(diagram of the solution in attached pic)

AB=Side of the square=S

AC = Diagonal of the square=Hypotenuse

As , we know that all sides of a square is equal,

therefore AB = BC =S

➡In a right angled ∆ABC

Using Pythagoras theorem,

=> (AC) ²=(AB) ²+(BC) ²

=> (10cm) ²=(S) ²+(S) ²

=>100cm²=S²+S²

=> 100cm²=2S²

=> 100/2cm²=S²

=>50cm²=S²

=> √50cm²= S

=> 5√2 =S

The length of side=5√2cm

More information ⤵

➡Perimeter of square=4×Side

➡Area of square= Side² or Side ×Side

➡Perimeter of rectangle=2(Length+Breath)

➡Area of rectangle= Length× Breath

Hope this is helpful to you!