Question

Question 95

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 property.

(ii) If x nails are used to repair one board, then 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, then 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

Given, length of bulletin board = r cm

breadth of bulletin board = t cm

Perimeter is defined as the sum of lengths of all sides of a planar figure.

$\therefore$ Perimeter of bulletin board =(r+t+r+t) cm = 2(r + t) cm

Area of a rectangle = length $\times$ breadth

$\therefore$ Area of bulletin board = $r\times t=rt{cm}^2$

(i) Since 10 cm extra strip is required, the total length of wire needed will be 10 cm more than the perimeter of the bulletin board.

$\therefore$ Required length of aluminlum strip = [2 (r + t) + 10] cm

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

$\therefore$ Number of nails required for 15 boards $=15x$

(iii) Area of one board = $rt{cm}^2$

Area of eight boards = 8 $\times$ area of one board = $8\times rt=8rt{cm}^2$

Given, extra cloth for one board = $500{cm}^2$

$\therefore$ Extra cloth for 8 boards = 500 $\times$ 8 = 4000 ${cm}^2$

(iv) Charges for one board = Rs.$x$

$\therefore$ Charges of 23 boards = Rs. $23\times x=23x$