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.

Answer 1

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"`