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Question
In an exhibition hall, there are 24 display boards each of length 1 m 50 cm and breadth 1 m. There is a 100 m long aluminium strip, which is used to frame these boards. How many square metres of cloth is required to cover all the display boards? What will be the length in m of the cloth used, if its breadth is 120 cm?
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Solution
Given, total display boards = 24
Length of display board = 1 m + 50 cm
= 1 m + `50/100` m ...[∵ 1 m = 100 cm]
= 1 m + `1/2` m
= `((2 + 1)/2)` m
= `3/2` m
Breadth of display board = 1 m
Now, area of one display board = Length × Breadth
= `1 xx 3/2`
= `3/2` sq.m
∴ Area of 24 display boards = 24 × Area of one board
= `24 xx 3/2`
= 36 sq.m
Hence, 36 sq.m cloth is required to cover all the display boards.
Now, breadth = 120 cm ...[Given]
∵ 1 cm = 100 cm
∴ 1 cm = `1/100` m
⇒ 120 cm = `120/100 = 6/5` m
Let length = `l` m
∵ Area of display board = Length × Breadth
`36 = l xx 6/5`
⇒ `(36 xx 5)/6 = l xx 6/5 xx 5/6` ...[Multiply both sides by `6/5`]
⇒ `l` = 30 m
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