Question

A square has each side of 5cm.find the length of one of its diagonals

Answer 1

Given :

Length of each side of square (a) = 5 cm

To Find :

Length of one of the diagonal of square.

Solution :

We know, a diagonal divides the square into two congruent right angled triangles, thus we can use Pythagoras theorem to find the length of the diagonal (which would be the hypotenuse of the right angled triangle).

Using Pythagoras Theorem,

∴    (Diagonal)²  =  (side)²  + (side)²

⇒    (Diagonal)² =  2×(side)²

⇒     Diagonal   =   √2 × (side)

⇒     Diagonal   =   √2 × 5

∴      Diagonal   =   7.07 cm

Therefore, the diagonal of the square is found to be 7.07 cm.

Answer 2

Answer:

Length of the diagonal is 7.071 cm.

Step-by-step explanation:

• In context to the given question we have, to find the length of the diagonal .
• Given;

1. That is a square
2. sides of square = 5cm

⇒ Let the square be ABCD given in the fig

and let the diagonal be BD

⇒ In ΔABD;

we know that

• Square has 90° all the angles ; therefore ΔABD is a right angle triangle;

By Pythagoras theorem;

⇒(hypotenuse)² = (base)²+(perpendicular)²

(BD)²=(AB)²+(AD)²

we know that the sides are 5

(BD)²=(5)²+(5)²

BD = √(25+25)

BD = √50

BD = 5√2 = 7.071 cm

∴ Length of the diagonal is 7.071 cm.