Perimeter of a Rhombus

A rhombus is a quadrilateral with all four sides of equal length. To find the perimeter of a rhombus, we need to know the length of one side.

Given that the lengths of the diagonals of the rhombus are 16 cm and 30 cm, we can use this information to find the length of one side and then determine the perimeter.

Finding the Length of a Side

In a rhombus, the diagonals intersect at a 90-degree angle, bisecting each other. This creates four congruent right triangles within the rhombus.

Let's label the length of one side of the rhombus as 's'.

Using the Pythagorean theorem, we can find the length of one side by considering one of the right triangles formed by the diagonals.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the length of the hypotenuse is the length of one of the diagonals, which is 30 cm. The other two sides of the right triangle are half the lengths of the diagonals, which are 16 cm and 15 cm.

Applying the Pythagorean theorem:

s^2 = (16/2)^2 + (15/2)^2
s^2 = 8^2 + 7.5^2
s^2 = 64 + 56.25
s^2 = 120.25

Taking the square root of both sides:

s = √120.25
s ≈ 10.96 cm

Calculating the Perimeter

Now that we know the length of one side of the rhombus is approximately 10.96 cm, we can calculate the perimeter by multiplying this length by 4.

Perimeter = 4 * 10.96 cm
Perimeter ≈ 43.84 cm

Conclusion

The perimeter of the rhombus is approximately 43.84 cm. This was determined by finding the length of one side using the Pythagorean theorem and then multiplying that length by 4 to account for all four sides of the rhombus.