Question

Length and breadth of a bulletin board are $rcm$ and $tcm$ respectively. [4 MARKS]

(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 each board, how many nails will be required to repair 15 such board?

(iii) If $500c{m}^2$ 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 1

Each Point: 1 Mark

Perimeter of the bulletin board $=2(r+t)cm$
Area of the bulletin board $=rtc{m}^2$

(i) Length (in cm) of the aluminium strip required to frame the board = Perimeter + extra strip
= $2(r+t)+10cm$

(ii) Repairing 1 board requires $x$ nails.
$\therefore$ Number of nails required to repair 15 boards = $15x$

(iii) Total area of cloth required = Area of 8 bulletin boards + Area of extra cloth required for 8 boards
= ($8\times r\times tc{m}^2$) + ($8\times 500c{m}^2$)
= ($8rt+4000)c{m}^2$

(iv) Carpenter's charge for making 1 board = Rs $x$
$\therefore$ Expenditure for making 23 boards = Rs $23x$