Диагонали ромба равны 24 см и 32см. Найдите периметр ромба.
The perimeter of a rhombus can be calculated by adding all four sides of the shape together. First, we need to find the length of the missing sides using the given diagonal lengths of the rhombus. To do this, we can use the Pythagorean theorem, which 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 two missing sides of the rhombus form two right triangles with the given diagonal lengths as their hypotenuses.
Let's label the sides of our right triangles as a, b, and c, where a and b are the lengths of the two missing sides and c is the length of the given diagonal. We can set up two equations using the Pythagorean theorem:
a² + b² = 24²
b² + c² = 32²
Solving these equations simultaneously, we get a = 4 and b = 16. Now, we can use the formula for the perimeter of a rhombus, which is P = 4a, where a is the length of one side.
P = 4(4) = 16cm
This means that the perimeter of the rhombus is 16 cm. Don't forget to label your answer with the correct unit of measurement!
