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Question
A thin metal iron-sheet is rhombus in shape, with each side 10 m. If one of its diagonals is 16 m, find the cost of painting both sides at the rate of ₹ 6 per m2. Also, find the distance between the opposite sides of this rhombus.
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Solution
Side of rhombus-shaped iron sheet = 10 m and one diagonals (AC) = 16 m
Join BD diagonal which bisects AC at O
The diagonals of a rhombus bisect each other at the right angle
∴ AO = OC = `16/2` = 8m.
Now in right ΔAOB
AB2 = AO2 + BO2 ⇒ (10)2 = (8)2 + BO2
⇒ 100 = 64 + BO2 ⇒ BO2 = 100 - 64 = 36
= (6)2
∴ BO = 6 m
∴ BD = 2 × BO = 2 × 6 = 12 m
Now, the area of rhombus = `(d_1 xx d_2)/2`
= `(16 xx 12)/2 = 96 "m"^2`
Rate of painting = ₹ 6 per m2
∴ The total cost of painting both sides,
= `2 xx 96 xx 6 = ₹ 1152`
Distance between two opposite sides,
= `"Area"/"Base" = 96/10 = 9.6 "m"`
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