A rhombus sheet whose perimeter is 260cm and whose one diagonal is 66cm is painted on both sides at the rate of 50 paise cm^2.Find the cost of painting.
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Answer: 147.84
Step-by-step explanation:
It is important to recall the properties of a rhombus. By definition, a rhombus has four sides of equal length and the diagonals intersect forming four right triangles whose hypotenuse is equal to the length of the rhombus.
Clearly, perimeter of a rhombus= 4x, where x is the length of the rhombus.
260cm=4x
X=65cm
Applying Pythagoras theorem, 65^2=y^2+ 33^2
y=56cm
56cm is one-half of the other diagonal of the rhombus.
Full length of the other diagonal= 2×56cm
=112cm
Finally, we are supposed to calculate the area of the rhombus= 1/2×ab
=1/2×112cm×66cm
=3696cm^2
Since it is painted both sides, we multiply by 2
Total area= 3696cm^2×2
=7392cm^2
Cost of painting=7392cm^2/50
=147.84
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