Question
A rhombus sheet, whose perimeter is 32m 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 $=32 m$
We know that, Perimeter of a rhombus $=4 \times$ side $4 \times$ side $=32 m 4 \times a =32 m$ a $=8 m$
Let $AC =10 m O A=12 \times ACOA =12 \times 10 OA =5 m$
By using Pythagoras theorem $O B^2=A B^2-O A^2 O B^2$
$=8^2-5^2$
$OB=\sqrt{39} m$
$BD=2 \times OBBD=2 \sqrt{39} m$
Area of the sheet $=\frac{1}{2} \times BD \times AC$
Area of the sheet $=\frac{1}{2} \times 2 \sqrt{39} \times 10$
Therefore, cost of printing on both sides at the rate of ₹ 5 per $m ^2=₹ 2 \times 10 \sqrt{39} \times 5$
$=₹ 625$.
We know that, Perimeter of a rhombus $=4 \times$ side $4 \times$ side $=32 m 4 \times a =32 m$ a $=8 m$
Let $AC =10 m O A=12 \times ACOA =12 \times 10 OA =5 m$
By using Pythagoras theorem $O B^2=A B^2-O A^2 O B^2$
$=8^2-5^2$
$OB=\sqrt{39} m$
$BD=2 \times OBBD=2 \sqrt{39} m$
Area of the sheet $=\frac{1}{2} \times BD \times AC$
Area of the sheet $=\frac{1}{2} \times 2 \sqrt{39} \times 10$
Therefore, cost of printing on both sides at the rate of ₹ 5 per $m ^2=₹ 2 \times 10 \sqrt{39} \times 5$
$=₹ 625$.
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