Length and breadth of a bulletin board are r cm and t cm, respectively.
(i) What will be the length (in cm) of the aluminium strip required to frame the board, if 10cm extra strip is required to fix it properly.
(ii) If x nails are used to repair one board, how many nails will be required to repair 15 such boards?
(iii) If 500sqcm extra cloth per board is required to cover the edges, what will be the total area of the cloth required to cover 8 such boards?
(iv) What will be the expenditure for making 23 boards, if the carpenter charges Rs x per board.
(i) 2(r + t) + 10
(ii) 15x
(iii) (8rt + 4000) sq cm
(iv) Rs 23x
Given: A rectangular bulletin board with length = (r) cm and breadth = (t) cm.
Idea: The strip goes around the border → this is the perimeter of a rectangle.
Perimeter of a rectangle:
( ext{Perimeter} = 2 imes ( ext{length} + ext{breadth}))
Put length = (r), breadth = (t):
(= 2 imes (r + t))
We need 10 cm extra to fix it properly, so add 10:
( ext{Total strip} = 2(r + t) + 10 ext{cm})
Answer (i): (2(r + t) + 10) cm
Idea: If one board needs (x) nails, then 15 boards need 15 times that number.
Number of nails:
( ext{Total nails} = 15 imes x)
Answer (ii): (15x) nails
Idea: Area of one rectangular board is length × breadth.
Area of one board:
( ext{Area} = r imes t)
Extra cloth per board:
(+,500 ext{sq cm})
Total cloth for one board:
(rt + 500)
For 8 boards, multiply by 8:
( ext{Total cloth} = 8 imes (rt + 500))
Expand (optional):
(= 8rt + 4000) sq cm
Answer (iii): (8rt + 4000) sq cm
Idea: Cost for many items = (cost for one) × (number of items).
Total cost:
( ext{Cost} = 23 imes x)
Answer (iv): Rs (23x)