Question

How many envelopes can be made out of a rectangular sheet of paper 9 m by 3 m, if each envelope requires a paper of size 18 cm by 12 cm?

Answer 1

Answer:

$\red\bigstar$ A total of 1250 envelopes can be made .

SOLUTION

Rectangular Sheet of Paper

Length of the rectangular sheet of paper = 9m = 9 × 100 = 900cm.

Breadth of the rectangular sheet of paper = 3m = 3 × 100 = 300cm.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 900 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 300cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Area of a rectangle = l × b , Where l is the length and b is the breadth of the rectangle.

Here,

l = 900 cm.

b = 300 cm.

⇒ Area of the rectangular sheet of paper  = 900 × 300

⇒ Area of the rectangular sheet of paper  = 270000 cm².

Envelope

Length of the envelope = 18cm.

Breadth of the envelope = 12cm.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 18 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 12cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Area of a rectangle = l × b , Where l is the length and b is the breadth of the rectangle.

Here,

l = 18cm.

b = 12cm.

⇒ Area of the envelope = 18 × 12

⇒ Area of the envelope = 216 cm².

$\boxed{\sf Number \: of \: envelope \: that \: can \: be \: made = \dfrac{Area \; of \; \; rectangular \; sheet \; of \; paper }{Area \: of \: the \: envelope} }$

Here,

Area of the rectangular sheet of paper  = 270000 cm².

Area of the envelope = 216 cm².

$\implies \sf Number \: of \: envelope \: that \: can \: be \: made = \dfrac{270000 }{216}$

$\implies \sf Number \: of \: envelope \: that \: can \: be \: made = 1250$

Answer 2

Step-by-step explanation:

$Answer:</p><p>\red\bigstar★ A total of 1250 envelopes can be made .</p><p></p><p>SOLUTION</p><p></p><p>Rectangular Sheet of Paper</p><p></p><p>Length of the rectangular sheet of paper = 9m = 9 × 100 = 900cm.</p><p>Breadth of the rectangular sheet of paper = 3m = 3 × 100 = 300cm.</p><p>\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 900 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 300cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}</p><p>Area of a rectangle = l × b , Where l is the length and b is the breadth of the rectangle.</p><p>Here,</p><p>l = 900 cm.</p><p>b = 300 cm.</p><p>⇒ Area of the rectangular sheet of paper  = 900 × 300</p><p>⇒ Area of the rectangular sheet of paper  = 270000 cm².</p><p></p><p>Envelope</p><p></p><p>Length of the envelope = 18cm.</p><p>Breadth of the envelope = 12cm.</p><p>\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 18 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 12cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}</p><p>Area of a rectangle = l × b , Where l is the length and b is the breadth of the rectangle.</p><p>Here,</p><p>l = 18cm.</p><p>b = 12cm.</p><p>⇒ Area of the envelope = 18 × 12</p><p>⇒ Area of the envelope = 216 cm².</p><p>\boxed{\sf Number \: of \: envelope \: that \: can \: be \: made = \dfrac{Area \; of \; \; rectangular \; sheet \; of \; paper }{Area \: of \: the \: envelope} }Numberofenvelopethatcanbemade=AreaoftheenvelopeAreaofrectangularsheetofpaper</p><p>Here,</p><p>Area of the rectangular sheet of paper  = 270000 cm².</p><p>Area of the envelope = 216 cm².</p><p>\implies \sf Number \: of \: envelope \: that \: can \: be \: made = \dfrac{270000 }{216}⟹Numberofenvelopethatcanbemade=216270000</p><p>\implies \sf Number \: of \: envelope \: that \: can \: be \: made = 1250⟹Numberofenvelopethatcanbemade=1250</p><p>$