The diagonals of a rhombus are in 2:1. If the perimeter of the rhombus is 120cm, find the length of the diagonals.

Perimeter = 120 cm

Length of each side = 120/4 = 30
Let the diagonals be x and 2x.

Use Pythagoras theorem to calculate each side in terms of the half diagonals, x/2 and x.

30 = sqrt((x/2)²+x²)
Square both sides:
900 = (x/2)²+x²=(5/4)x²
x²=720
x=?

To find the length of the diagonals of a rhombus, we need to use the given information about the ratios and the perimeter.

Step 1: Let's assume that the shorter diagonal is represented by 2x and the longer diagonal is represented by x. This is based on the given ratio of 2:1.

Step 2: The perimeter of a rhombus is defined as four times the length of one side. Therefore, the length of one side would be: (120 cm) / 4 = 30 cm.

Step 3: In a rhombus, the diagonals bisect each other at right angles, forming four right-angled triangles.

Step 4: Applying the Pythagorean theorem to one of the right-angled triangles, we can find the relationship between the sides using the given ratios. The sides of the right-angled triangle would be half of the diagonals and half the length of one side.

Step 5: Using the Pythagorean theorem: (2x/2)^2 + (x/2)^2 = (30/2)^2
Simplifying this equation: x^2 + x^2 = 15^2
2x^2 = 225
x^2 = 112.5
x = √112.5

Therefore, the length of the longer diagonal (x) is approximately 10.61 cm and the length of the shorter diagonal (2x) is approximately 21.21 cm.