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Question
A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.
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Solution
Given that,
Perimeter of a rhombus = 32 m
We know that,
Perimeter of rhombus = 4 × side
⇒ 49 = 32m
⇒ a = 8 m
Let AC = 10 = OA = `1/2`𝐴𝐶
= `1/2`×10
= 5𝑚
By using Pythagoras theorem:
∴`OB^2=AB^2-OA^2`
`⇒OB=sqrt(AB^2-OA^2)`
`⇒OB=sqrt(8^2-5^2)`
`⇒OB=sqrt(64-25)`
`⇒OB=sqrt(39m)`
Now, BD = 2OB = 2√39𝑚
∴ Area of sheet = `1/2`×𝐵𝐷×𝐴𝐶=`1/2`×2`sqrt(39)xx10sqrt(39)m^2`
∴ Cost of printing on both sides at the rate of Rs 5 per `m^2` = Rs 2 ×10`sqrt(39)`×5
= Rs. 625.00
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