a rhombus sheet whose perimeter is 32 m and whose one diagonals is10 m long is painted on both sides - Maths - Heron\s Formula

Question

a rhombus sheet whose perimeter is 32 m and whose one diagonals
is10 m long is painted on both sides at the rate of RS 5m square(2)
,find the cost of painting??

Ankush Jain · Accepted Answer

Given, perimeter of rhombus sheet = 32m â‡’ 4 (side) = 32m â‡’ side = 8m So, the side of rhombus is 8m We know that the diagonals of a rhombus bisect each other at right angle So, in right triangle OAB, we have $(AB)^{2} = {(OA)}^{2} + (OB)^{2} \Rightarrow (8)^{2} = {(OA)}^{2} + 5^{2} \Rightarrow {(OA)}^{2} = 64 - 25 = 39 \Rightarrow OA = \sqrt{39} \Rightarrow AC = 2 (O A) = 2 \sqrt{39} m$ Area of rhombus = $\frac{1}{2}$ (product of diagonals) = $\frac{1}{2}$ (AC Ã— BD) $= \frac{1}{2} (2 \sqrt{39} \times 10) = 10 \sqrt{39} m^{2}$ Given, cost of painting = Rs 5/m2 âˆ´ cost of painting 2 side of rhombus sheet = 2 [Area of rhombus Ã— cost of painting per m2] $= 2 \times 10 \sqrt{39} \times 5 = Rs 100 \sqrt{39} = Rs 624 49$

a rhombus sheet whose perimeter is 32 m and whose one diagonals is10 m long is painted on both sides at the rate of RS 5m square(2) ,find the cost of painting??