Question
A rhombus sheet, whose perimeter is $32\ m$ and whose diagonal is $10m$ long, is painted on both the sides at the rate of ₹ $5$ per meter square. Find the cost of painting.
✓
Answer
Given that, Perimeter of a rhombus $= 32m$
We know that, Perimeter of a rhombus $= 4 \times$ side $4 \times$ side $= 32m\ 4 \times a = 32m a = 8m$ Let $AC = 10m$
$OA = 12 \times AC OA = 12 \times 10 OA = 5m$
By using Pythagoras theorem $OB^2 = AB^2 − OA^2 OB^2 = 8^2 − 5^2$
$\text{OB}=\sqrt{39}\text{m}$
$BD = 2 \times OB$
$\text{BD}=2\sqrt{39}\text{m}$ Area of the sheet $=\frac{1}{2}\times\text{BD}\times\text{AC}$
Area of the sheet $=\frac12\times2\sqrt{39}\times10$
Therefore, cost of printing on both sides at the rate of $₹ 5$ per $m^2$
$=₹2\times10\sqrt{39}\times5$
$= ₹ 625.$
We know that, Perimeter of a rhombus $= 4 \times$ side $4 \times$ side $= 32m\ 4 \times a = 32m a = 8m$ Let $AC = 10m$
$OA = 12 \times AC OA = 12 \times 10 OA = 5m$
By using Pythagoras theorem $OB^2 = AB^2 − OA^2 OB^2 = 8^2 − 5^2$
$\text{OB}=\sqrt{39}\text{m}$
$BD = 2 \times OB$
$\text{BD}=2\sqrt{39}\text{m}$ Area of the sheet $=\frac{1}{2}\times\text{BD}\times\text{AC}$
Area of the sheet $=\frac12\times2\sqrt{39}\times10$
Therefore, cost of printing on both sides at the rate of $₹ 5$ per $m^2$
$=₹2\times10\sqrt{39}\times5$
$= ₹ 625.$
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