The area of the square is 49 cm. What is the diagonal of the square?

So, we know the area of the square. We can find the lengths of its sides, because we know that all sides of a square are equal.
√49 = 7 – the length of one side;
I propose to find out the length of the diagonal of a square using the Pythagorean theorem.
The diagonal divides the square into two equal right-angled triangles, in which the sides of the square act as legs, and the diagonal acts as the hypotenuse.
So the diagonal in the square will be equal to the sum of the squares of the sides:
7² + 7² = 49 + 49 = 98;
√98 = 7√2 – the length of the diagonal of the square;
Answer: 7√2.