In a rhombus with side √52, half of one diagonal is 4. Find the second diagonal of the rhombus.

Let’s use the following properties of rhombus diagonals:

1) the intersection point divides the diagonals in half;

2) the diagonals of the rhombuses are perpendicular.

Then the square of the second half of the diagonal is easy to find by the Pythagorean theorem:

(√52) ^ 2 – 4 ^ 2 = 52 -16 = 36.

And the whole diagonal is equal to:

2 * √36 = 12.