Find the diagonal of a square if its area is 98.

We know that a square is a rectangle with equal sides and its diagonals (d) are equal. The diagonal (d) divides the square into two equal parts, which are equal right-angled triangles with the values ​​of the legs equal to the side of this square, and the hypotenuse is equal to the diagonal of the square. That is, we have a right-angled triangle where the legs are equal to each other.
We know the area of ​​a square is equal to 98 cm square.
The formula for finding this area is:

S = a * a = a ^ 2.

From the Pythagorean theorem for a right-angled triangle, we can find the value of the hypotenuse, which is the diagonal of the square.

c ^ 2 = a ^ 2 + b ^ 2 – where a and b are legs of a triangle, and in our case they are equal. And c – the hypotenuse, it is also the diagonal.
Then c ^ 2 = a ^ 2 + a ^ 2 = 2 * a ^ 2
But a ^ 2 = S:
c ^ 2 = 2 * S
c = √ (2 * S) = d

Substitute the area value and get the desired diagonal value:
d = √ (2 * 98) = √196 = 14 cm.

The answer is the diagonal of the square is 14 cm.