Find the diagonal of a square if its area is 25 cm2 and 30 cm2.

1. If the area of the square is 25 cm ^ 2, then by the formula S = a ^ 2, where a is the side of the square, we find its side:

25 = a ^ 2;

a = √25 = 5 (see)

2. The diagonal of the square is the hypotenuse of the resulting right-angled triangles, and the sides of the square are the legs of the triangles. By the Pythagorean theorem for the square 2a ^ 2 = c ^ 2, where a – legs, c – hypotenuse, we find the diagonal:

c = √ (2 * 5 ^ 2) = √50 = 5√2 (cm).

3. If the area of the square is 30 cm ^ 2, then:

30 = a ^ 2;

a = √30 (see)

4. Find the diagonal:

c = √ (2 * (√30) ^ 2) = √60 = 2√15 (cm).