The sides of the rhombus are 29 cm and one of the diagonals is 42 cm, which is equal to the second diagonal.

It is known from the condition that the sides of the rhombus are 29 cm, and one of the diagonals is 42 cm. Find what is the second diagonal of the rhombus.

To do this, we apply the Pythagorean theorem to a right-angled triangle, which is formed by the side of the rhombus (hypotenuse) and the halves of the diagonals of the rhombus (legs). The diagonals of the rhombus intersect at right angles.

We know the length of the hypotenuse is 29 cm and the length of one leg is 42: 2 = 21 cm. We are looking for the length of the second leg:

b = √ (c ^ 2 – a ^ 2) = √29 ^ 2 – 21 ^ 2 = √ (29 – 21) (29 + 21) = √ (8 * 50) = √ (4 * 100) = 2 * 10 = 20 cm.

20 * 2 = 40 cm length of the second diagonal.