Question

19. Establish de relation between diagonal and side of a square.
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Answer 1

Square has all its sides equal. All its angles are right angles. So each of the diagonal divides the square into 2 triangles.

Thus by Pythagoras theorem,

a²+a² = diagonal ²

Diagonal = √2a²

Diagonal = √2a where a is the side of the square.

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Answer 2

Answer:

Side ( a ) = diagonal ( a√2)

Step-by-step explanation:

Let the side of square ABCD be a.

So the diagonal of square = AC =AD

We know that each angle of square is 90°. Then, AC and AD will be hypotenuse.

So in right triangle ABC,

By Pythagoras Theorem,

(AC)^2 = (AB)^2 + (BC)^2

(AC)^2 = (a)^2 + (a)^2

(AC)^2 = 2a^2

AC = √2 a

AC = a√2

Hence,diagonal of the square =a√2

(where 'a' is the side of the square).