In the above question, 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?
Cloth required = 36 m²; Length of cloth = 30 m
Step 1: Find total cloth area needed.
Area of one display board = (1.5 ext{m}^2).
Number of boards = (24).
Total area = (24 imes 1.5 ext{m}^2).
Compute it in parts:
(1.5 imes 20 = 30)
(1.5 imes 4 = 6)
So, (30 + 6 = 36 ext{m}^2).
Cloth required to cover all boards = (36 ext{m}^2).
Step 2: Convert the breadth of cloth to metres.
Given breadth = (120 ext{cm}).
(120 ext{cm} = dfrac{120}{100} ext{m} = 1.2 ext{m}).
Step 3: Use the area formula to find the length of cloth.
For a rectangle: ( ext{Area} = ext{Length} imes ext{Breadth}).
So, ( ext{Length} = dfrac{ ext{Area}}{ ext{Breadth}}).
Substitute values:
( ext{Length} = dfrac{36}{1.2} ext{m}).
Divide neatly by removing the decimal:
(dfrac{36}{1.2} = dfrac{360}{12} = 30 ext{m}).
Final Answer:
Cloth required = (36 ext{m}^2).
Length of the cloth (breadth (= 1.2 ext{m})) = (30 ext{m}).