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

Let ABCD be a square. The area of a square is found by the formula:
S = t ^ 2,
where S is the area of the square, t is the length of the side of the square.
Let’s find the length of the side of the square:
t ^ 2 = 98;
t = √98;
t = 7√2 (conventional units).
The diagonal of the square ABCD divides it into two identical right-angled triangles ABD and BCD. Consider a triangle ABD. ABD is an isosceles right-angled triangle, since its legs AB and AD are equal, because they are the sides of a square. Find the hypotenuse BD of triangle ABD by the Pythagorean theorem:
BD = √ (AB ^ 2 + AD ^ 2) = √ ((7√2) ^ 2 + (7√2) ^ 2) = √ (98 + 98) = √196 = 14 (cm).
Answer: the diagonal is 14 cm.