A RHOMBUS SHAPED SHEET WITH PERIMETER 40 CM. AND ONE DIAGONAL 12 CM., IS PAINTED ON BOTH SIDES AT THE RATE OF RS.5 PER METER SQUARE. FIND COST OF PAINTING.
The other diagonal is 16
area = 1/2 d1*d2 = 1/2 * 12 * 16 = 96 cm^2
cost = RS 2*.5/m^2 * 96 cm^2 * (1m/100cm)^2 = RS 0.0096
Might small number?
$ 960
To find the cost of painting the rhombus-shaped sheet, we need to find its area first.
Since the rhombus has a perimeter of 40 cm, we know that the sum of all its sides is 40 cm. Since a rhombus has all sides equal in length, each side of the rhombus is 40 cm divided by 4, which is 10 cm.
Now that we know the length of one side of the rhombus, we can calculate its area. The area of a rhombus can be found using the formula: Area = (diagonal 1 * diagonal 2) / 2.
We are given that one diagonal of the rhombus is 12 cm. Let's assume that the other diagonal is x cm. Since any two diagonals of a rhombus are perpendicular bisectors of each other, we can use the Pythagorean Theorem to find the length of the other diagonal.
The Pythagorean Theorem 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 our case, the diagonals of the rhombus form a right triangle. So, we can use the Pythagorean Theorem as follows:
x^2 = (10/2)^2 + (12/2)^2
x^2 = 5^2 + 6^2
x^2 = 25 + 36
x^2 = 61
x = sqrt(61)
x ≈ 7.81 cm
Now that we know both diagonals, we can calculate the area of the rhombus:
Area = (12 * 7.81) / 2
Area ≈ 93.72 cm²
Since the sheet is painted on both sides, the total area to be painted is twice the area of the rhombus:
Total Area = 2 * 93.72 cm²
Total Area ≈ 187.44 cm²
Now, we can calculate the cost of painting. We are given that the rate is Rs.5 per square meter. To convert our area from square cm to square meters, we divide by 10000 (since there are 10000 square centimeters in a square meter):
Total Area in square meters = 187.44 cm² / 10000
Total Area in square meters ≈ 0.018744 m²
Cost of painting = Total Area in square meters * Rate
Cost of painting ≈ 0.018744 m² * Rs.5/m²
Cost of painting ≈ Rs.0.09372
Therefore, the cost of painting the rhombus-shaped sheet is approximately Rs.0.09372.