Question

What will be the ratio of the side
and the diagonal of a square ?
​

Answer 1

Answer:

it is 1:root2

Step-by-step explanation:

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Answer 2

Answer:

Let us start by taking a square ABCD with each of its sides measuring a unit. Also, we let the length of the diagonals to be l units.

Now let us draw the diagram of the square ABCD with all the assumed lengths for better visualisation.

As we know that all the sides of a square are equal and each of the interior angle measures 90∘90∘ , we can say that ΔABCΔABC is a right isosceles triangle with measure of the base and perpendicular equal to a units and AC being the hypotenuse, i.e., hypotenuse is equal to l units.

Now applying the Pythagoras theorem for right angled triangles, we get

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

⇒AB2+BC2=AC2⇒AB2+BC2=AC2

⇒a2+a2=l2⇒a2+a2=l2

⇒2a2=l2⇒2a2=l2

Taking square root of both the sides of the equation will give us:

l=2–√a l=2a