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) We have to frame the perimeter of the board hence length of aluminium strip required to frame the board will be same as perimeter of board Perimeter of board = 2 × (r + t)

But 10 cm extra strip is required to fix it properly hence we should add 10 to perimeter of board

Therefore, aluminium strip required to frame the board is 2 × (r + t) + 10 cm

(ii) Number of nails required to repair 1 board = x

Number of nails to repair 15 boards = 15 × Number of nails required to repair 1 board

Number of nails to repair 15 boards = 15 × x = 15x

(iii) Area of one board = r × t sq. cm

500 sq. cm extra cloth is required per board so we should add 500 in area of one board to get the total area of cloth required for one board

Area of cloth required for one board = Area of one board + 500 sq. cm

Therefore, Area of cloth required for one board = (r × t) + 500 sq. cm

Area of cloth required for 8 boards = 8 × Area of cloth required for one board

Area of cloth required for 8 boards = 8 × [(r × t) + 500]

= 8(r × t) + 4000 sq. cm

Therefore, Area of cloth required for 8 boards = 8(r × t) + 4000 sq. cm

(iv) Expenditure of making 1 board = x Rs

Expenditure of making 23 boards = 23 × Expenditure of making 1 board = 23 × x = 23x

Therefore, Expenditure of making 23 boards = 23x