A rhombus sheet,whose perimeter is 32 m and whose one diagonal is 10 m long , is painted on both the sides of Rs.5 per m^2.Find the cost of the painting
Since the diagonals of a rhombus are perpendicular, and all four sides are the same length, the rhombus can be divided into four right triangles with one leg of 5 and an hypotenuse of 8. So, the other leg is √39
So, the area of all four triangles is 10√39 m^2
Multiply that by the cost of the paint.
To find the cost of painting the rhombus sheet, we first need to find the area of the sheet.
Since a rhombus has equal sides, the perimeter of the rhombus is given by 4 times the length of one side. The formula is:
Perimeter = 4 * Length of one side
Given that the perimeter is 32 m, we can write the equation as:
32 = 4 * Length of one side
Dividing both sides by 4, we find:
Length of one side = 32 / 4 = 8 m
Now, let's find the area of the rhombus using the formula:
Area = (Product of diagonals) / 2
We are given that one diagonal is 10 m long. Let's call the other diagonal 'x'. Since the diagonals of a rhombus bisect each other at 90 degrees, we can use the Pythagorean theorem to find the length of 'x'.
Using the Pythagorean theorem:
x^2 = (8/2)^2 - (10/2)^2
x^2 = 16 - 25
x^2 = -9
Since the value under the square root is negative, it means that the other diagonal 'x' cannot have a real value. This is not possible for a rhombus.
Therefore, it appears that there is an error in the given information, as there is no real solution for the diagonals of the rhombus.
Without the correct length of the other diagonal, we cannot calculate the area or the cost of painting the rhombus sheet.