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?

Answer 1

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