text: # 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 $Rs.\ 5\ per\ m^2$. Find the cost of painting.
  
  Given:
  
  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 $Rs.\ 5\ per\ m^2$.
  
  To do:
  
  We have to find the cost of the painting.
  
  Solution:
  
  Length of each side of the rhombus $=\frac{32}{4}$
  
  $= 8\ m$
  
  Length of one of the diagonals $AC = 10\ m$
  
  In $\triangle ABC$,
  
  $a=8\ m, b= 8\ m, c= 10\ m$
  
  $s=\frac{a+b+c}{2}$
  
  $=\frac{8+8+10}{2}$
  
  $=\frac{26}{2}$
  
  $=13$
  
  Area of the triangle $ABC=\sqrt{s(s-a)(s-b)(s-c)}$
  
  $=\sqrt{13(13-8)(13-8)(13-10)}$
  
  $=\sqrt{13 \times 5 \times 5 \times 3}$
  
  $=5 \sqrt{39} \mathrm{~m}^{2}$
  
  Area of one sides of sheet $=2 \times 5 \sqrt{39}$
  
  $=10 \sqrt{39} \mathrm{~m}^{2}$
  
  Area of both sides of the sheet $=2 \times 10 \sqrt{39}$
  
  $=20 \sqrt{39}$
  
  $=20 \times 6.25$
  
  $=125.0 \mathrm{~m}^{2}$
  
  Rate of polishing both the sides of the sheet $= Rs. \5$ per $\mathrm{m}^{2}$
  
  Total cost of polishing $=Rs. 125 \times 5$
  
  $= Rs.\ 625$.
  
  Tutorialspoint
  
  Simply Easy Learning
  
  Updated on: 10-Oct-2022
  
  23 Views
explanation: The document contains a math problem and its solution. The problem involves calculating the cost of painting a rhombus sheet given its perimeter, one diagonal, and the painting rate. The solution is provided step-by-step, leading to the final cost of painting.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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 $Rs.\ 5\ per\ m^2$. Find the cost of painting.
  
  Given:
  
  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 $Rs.\ 5\ per\ m^2$.
  
  To do:
  
  We have to find the cost of the painting.
  
  Solution:
  
  Length of each side of the rhombus $=\frac{32}{4}$
  
  $= 8\ m$
  
  Length of one of the diagonals $AC = 10\ m$
  
  In $\triangle ABC$,
  
  $a=8\ m, b= 8\ m, c= 10\ m$
  
  $s=\frac{a+b+c}{2}$
  
  $=\frac{8+8+10}{2}$
  
  $=\frac{26}{2}$
  
  $=13$
  
  Area of the triangle $ABC=\sqrt{s(s-a)(s-b)(s-c)}$
  
  $=\sqrt{13(13-8)(13-8)(13-10)}$
  
  $=\sqrt{13 \times 5 \times 5 \times 3}$
  
  $=5 \sqrt{39} \mathrm{~m}^{2}$
  
  Area of one sides of sheet $=2 \times 5 \sqrt{39}$
  
  $=10 \sqrt{39} \mathrm{~m}^{2}$
  
  Area of both sides of the sheet $=2 \times 10 \sqrt{39}$
  
  $=20 \sqrt{39}$
  
  $=20 \times 6.25$
  
  $=125.0 \mathrm{~m}^{2}$
  
  Rate of polishing both the sides of the sheet $= Rs. \5$ per $\mathrm{m}^{2}$
  
  Total cost of polishing $=Rs. 125 \times 5$
  
  $= Rs.\ 625$.
  
  Tutorialspoint
  
  Simply Easy Learning
  
  Updated on: 10-Oct-2022
  
  23 Views
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math problem and its solution. The problem involves calculating the cost of painting a rhombus sheet given its perimeter, one diagonal, and the painting rate. The solution is provided step-by-step, leading to the final cost of painting.
  
  Label: question-and-answer