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 ` 5 Per M2. Find The Cost Of Painting.

Sol:

Perimeter = 32 m.

Therefore,

The length of a side = \(\frac{32}{4} \)= 8m.

Diagonal of a rhombus = 10m.

As we know;

The halves of diagonals and the sides of a rhombus form a right-angled triangle with the side as the hypotenuse.

Let the length of the other diagonal =2x.

\(x^{2} + (\frac{10}{2})^{2} = 8^{2}\\\Rightarrow x^{2} + (\frac{100}{4}) = 64\\\Rightarrow x^{2} + 25 = 64\\\Rightarrow x^{2} = 64 – 25\\\Rightarrow x^{2} = 39\\\Rightarrow x = \sqrt{39}\)

The measure of the another diagonal of the rhombus = \(2 * \sqrt{39} = 2\sqrt{39} m\)

So, Area of the rhombus = \(\frac{1}{2}\) * Diagonal of a rhombus * Measure of the another diagonal.

A = \(\frac{1}{2}\) * 10 * 2 \(\sqrt{39}\)

A = 62.45 m2.

Painted on both sides at the rate of Rs 5 per m2.

Cost = Area of both side * 5

= 2 * 62.45 * 5

= 124.9 * 5

= 624.50 = Rs 625.

Therefore, the cost of the painting is Rs. 625.

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