Given:
Perimeter of rhombus = 32m
Length of one diagonal = 10m
Rate of painting = Rs.5/m²

To Find:
Cost of painting the rhombus

Solution:
To find the cost of painting the rhombus, we need to calculate the area of the rhombus and then multiply it by the rate of painting.

Step 1: Find the Side Length of the Rhombus
The perimeter of a rhombus is the sum of all four sides. In this case, the perimeter is given as 32m. Since all sides of a rhombus are equal, we can divide the perimeter by 4 to find the length of each side.
Perimeter of rhombus = 4 * Side length
32m = 4 * Side length
Side length = 32m / 4
Side length = 8m

Step 2: Find the Area of the Rhombus
The area of a rhombus can be calculated using the formula: Area = (1/2) * Product of the diagonals.
In this case, we are given the length of one diagonal as 10m. To find the length of the other diagonal, we can use the properties of a rhombus.
Since the diagonals of a rhombus bisect each other at right angles, we can divide the rhombus into four congruent right triangles. The length of one side is 8m, and the length of one diagonal is 10m. Using the Pythagorean theorem, we can find the length of the other side of the right triangle (half of the other diagonal).
Let the length of the other side be x.
Using Pythagorean theorem:
x² + 8² = 10²
x² + 64 = 100
x² = 100 - 64
x² = 36
x = √36
x = 6m

Therefore, the length of the other diagonal is 2 * 6m = 12m.

Using the formula for the area of the rhombus:
Area = (1/2) * 10m * 12m
Area = 60m²

Step 3: Find the Cost of Painting
Now that we have the area of the rhombus, we can calculate the cost of painting.
Cost of painting = Area * Rate of painting
Cost of painting = 60m² * Rs.5/m²
Cost of painting = Rs.300

Therefore, the cost of painting the rhombus is Rs.300.