Question

Діагоналі ромба дорівнюють 16 см і 30 см. Знайти периметр ромба.

Answer 1

Finding the Perimeter of a Rhombus

To find the perimeter of a rhombus, we need to know the lengths of its diagonals. In this case, the diagonals of the rhombus are given as 16 cm and 30 cm.

The perimeter of a rhombus can be calculated by multiplying the length of one side by 4. Since the sides of a rhombus are congruent, we can find the length of one side by using the Pythagorean theorem.

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

Using the Pythagorean theorem, we can find the length of one side as follows:

s^2 = (d1/2)^2 + (d2/2)^2

Where: - s is the length of one side of the rhombus - d1 is the length of the first diagonal - d2 is the length of the second diagonal

Substituting the given values, we have:

s^2 = (16/2)^2 + (30/2)^2

Simplifying the equation:

s^2 = 8^2 + 15^2

s^2 = 64 + 225

s^2 = 289

Taking the square root of both sides:

s = √289

s = 17

Therefore, the length of one side of the rhombus is 17 cm.

Now, we can calculate the perimeter of the rhombus by multiplying the length of one side by 4:

Perimeter = 4 * s

Perimeter = 4 * 17

Perimeter = 68

Therefore, the perimeter of the given rhombus is 68 cm.