A rhombus-shaped sheet with perimeter 40cm and one diagonal 12 cm, is painted on both sides at the rate of Rs. 5 per m2. Find the cost of painting

Sure, let's solve this step by step.

Step 1: Understand the problem We have a rhombus-shaped sheet with a perimeter of 40 cm and one diagonal of 12 cm. We need to find the cost of painting both sides of this sheet.

Step 2: Find the length of the sides of the rhombus Since the perimeter of a rhombus is the sum of all its sides and all sides of a rhombus are equal, each side of the rhombus is 40 cm / 4 = 10 cm.

Step 3: Find the length of the other diagonal We know that in a rhombus, the diagonals are perpendicular bisectors of each other. So, they divide the rhombus into four right-angled triangles. We can use the Pythagorean theorem to find the length of the other diagonal. Let's denote the length of the other diagonal as d. Then, (d/2)^2 = 10^2 - (12/2)^2 = 100 - 36 = 64. So, d = 2 * sqrt(64) = 16 cm.

Step 4: Find the area of the rhombus The area of a rhombus is given by the formula 1/2 * product of diagonals = 1/2 * 12 cm * 16 cm = 96 cm^2.

Step 5: Convert the area into square meters 1 m^2 = 10,000 cm^2. So, the area of the rhombus in square meters is 96 cm^2 / 10,000 = 0.0096 m^2.

Step 6: Find the total area to be painted Since both sides of the sheet are to be painted, the total area to be painted is 2 * 0.0096 m^2 = 0.0192 m^2.

Step 7: Find the cost of painting The cost of painting is Rs. 5 per m^2. So, the total cost of painting is Rs. 5 * 0.0192 = Rs. 0.096.

So, the cost of painting the rhombus-shaped sheet on both sides is Rs. 0.096.