The diagonals of the rhombus are 3: 4, and its perimeter is 6m. Calculate the lengths of the diagonals of the rhombus.

Let’s calculate what the side of this geometric figure is equal to – a rhombus:

6: 4 = 1.5.

Let us denote by the variable k the length of half of the first diagonal of the rhombus.

Therefore, we can represent half of the second diagonal of the rhombus as 3k / 4.

Using the well-known formula from the Pythagorean theorem, we write the equation and find the lengths of the diagonals:

k ^ 2 + (3k / 4) ^ 2 = 1.52;

k ^ 2 + 9k ^ 2/16 = 2.25;

25k ^ 2 = 36;

k ^ 2 = 36/25;

k1 = 6/5;

k2 = -6/5;

6/5 * 2 = 2.4;

2.4 * 3/4 = 1.8.

Answer: The first diagonal is 2.4 centimeters, the second is 1.8.