Question

thin metal iron sheet is a rhombus in shape with each side 10 metre if one of its diagonals is 16 metre find the cost of painting its both sides at the rate of rupees 6 per metre square also find the distance between the opposite sides of this rhombus ​

Answer 1

Solution :-

Each side of the rhombus = 10 m

Let the rhombus be ABCD and d1 = 16 m and d2 = ?

In Δ ADC 

⇒ a = AD = 10 m, b = AC = 16 m and c = DC = 10 m

Semi perimeter = s = (a + b + c)/2

⇒ (10 + 16 + 10)/2

⇒ 36/2

⇒ 18 m

Area of Δ ADC = √s(s - a)(s - b)(s -c)

⇒ √18(18 - 10)(18 - 16)(18 - 10)

⇒ √18*8*2*8

⇒ √2304

⇒ Area of Δ ADC = 48 m²

Area of Δ ADC = Area of Δ ABC

So, area of Δ ABC = 48 m²

Total area = 48 + 48 = 96 m²

Area of rhombus = (d1 × d2)/2

⇒ 96 = (16 × d2)/2

⇒16d2 = 96*2

⇒ d2 = 192/16

⇒ d2 = 12 m

Cost of painting both sides of the rhombus = Rs. 6 m²

Area of both the sides of the rhombus = 96*2 = 192 m²

Total cost of painting both the sides of rhombus = 192*6

Total cost of painting both the sides of rhombus = Rs. 1152

Answer.