Length and breadth of a bulletin board are r cm and t cm, respectively

1.	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 10 cm 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 500 sq cm 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.
Answer» We have given, length of the board = r cm and breadth = t cm. (i) The length of aluminium strip to frame the board = Perimeter of the board = 2(length + breadth) = 2(r + t) cm But 10 cm extra strip is required to fix it properly. ∴ Total length of the aluminium strip = 2(r + t) cm + 10 cm. (ii) Number of nails required to repair 1 board = x. ∴ Number of nails required to repair 15 boards = 15 × x = 15x. (iii) Area of the cloth required for 1 board = Area of the board = length × breadth = r cm × t cm = (rt) sq cm Area of the cloth required for 8 boards = 8 × (rt) sq cm = 8rt sq cm But 500 sq cm extra cloth per board is required to cover the edges. ∴ For 8 boards we need 8 × 500 sq cm = 4000 sq cm extra cloth. Thus, the total area of the cloth required = (8rt + 4000) sq cm (iv) The carpenter charges for 1 board = Rs. x. ∴ The carpenter charges for 23 boards = Rs. (23 × x) = Rs. 23x

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 10 cm 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 500 sq cm 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.

Answer»

We have given, length of the board = r cm and breadth = t cm.

(i) The length of aluminium strip to frame the board

= Perimeter of the board

= 2(length + breadth)

= 2(r + t) cm

But 10 cm extra strip is required to fix it properly.

∴ Total length of the aluminium strip = 2(r + t) cm + 10 cm.

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

∴ Number of nails required to repair 15 boards = 15 × x = 15x.

(iii) Area of the cloth required for 1 board = Area of the board

= length × breadth

= r cm × t cm

= (rt) sq cm

Area of the cloth required for 8 boards

= 8 × (rt) sq cm

= 8rt sq cm

But 500 sq cm extra cloth per board is required to cover the edges.

∴ For 8 boards we need 8 × 500 sq cm

= 4000 sq cm extra cloth.

Thus, the total area of the cloth required

= (8rt + 4000) sq cm

(iv) The carpenter charges for 1 board = Rs. x.

∴ The carpenter charges for 23 boards

= Rs. (23 × x) = Rs. 23x