Question

what is the length of diagonal of a square of side 10 cm?​

Answer 1

Answer:

Step-by-step explanation:

ABCD is an Square having length of sides a and d is its diagonal.

Here sides AB = BC = CD = DA = a = 10 cm

Now consider the triangle ABC,which is a right angle triangle with ∠B = 90°

By Pythagoras theorem

AC² = AB² + BC²

d² = a² + a²

d² = (10cm)² + (10cm)²

d² = 200 cm²

So, d = √ (200cm²) = (10√ 2)cm

Now because every squares have two diagonals of equal length, So Diagonal AC = BD = d = (10√ 2)cm

Answer 2

AnSwer -:

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Length of diagonal of square-: 10√2 cm

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Step by Step Explanation-:


Given ,

Length of side of a square-: 10 cm

To find ,

Length of diagonal of a square.

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We know that ,

The all sides of square equal in length.

And ,

The all angles of a square makes right

Angled triangle.

And ,

Diagonal of a square divide square into

two right angled triangle.

Then ,

Diagonal will be the hypotenuse of the

Right angled triangle.

By Pythagoras theorem -:

(Hypotenuse )^2 = (Base)^2 +

(Perpendicular)^2

Base = 10 cm

Perpendicular = 10cm (all sides of

triangle are equal)

(Hypotenuse)^2 = (10)^2 + (10)^2

(Hypotenuse)^2 = 100 + 100


(Hypotenuse)^2 = 200

(Hypotenuse) = 10√2

Hypotenuse = 10√2cm

Therefore,

Hypotenuse = Diagonal of square =

10√2 cm

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Length of diagonal of square-: 10√2 cm

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