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The length and breadth of a cardboard are $2 \frac{1}{5} m$ and $1 \frac{1}{5} m$. respectively. The length and breadth of a second cardboard are $3 \frac{1}{5} m$ and $2 \frac{2}{5} m$ respectively. Both cardboards are divided into 10 equal small pieces. What is the total area of cardboard, if it is made using 5 smaller pieces from the first cardboard and 3 smaller pieces from the second cardboard ?
Given :
Length of the 1st cardboard $=2 \frac{1}{5} m$
Breadth of the 1st cardboard $=1 \frac{1}{5} m$
Length of the 2nd cardboard $= 3 \frac{1}{5} m$
Breadth of the 2nd cardboard $=2 \frac{2}{5} m$
To do :
We have to find the total area of the cardboard made from 5 small pieces of 1st cardboard and 3 small pieces of 2nd cardboard
Solution :
Length of the 1st cardboard $=2 \frac{1}{5} m= \frac{2\times5+1}{5} m = \frac{11}{5} m$
Breadth of the 1st cardboard $=1 \frac{1}{5} m= \frac{1\times5+1}{5} m = \frac{6}{5} m$
Area of a rectangle of length l and breadth b $= l\times b$
Area of the 1st cardboard $= \frac{11}{5} \times \frac{6}{5} = \frac{66}{25} m^2$ .
Length of the 2nd cardboard $=3 \frac{1}{5} m= \frac{3\times5+1}{5} m = \frac{16}{5} m$
Breadth of the 2nd cardboard $=2 \frac{2}{5} m= \frac{2\times5+2}{5} m = \frac{12}{5} m$
Area of the 2nd cardboard $= \frac{16}{5} \times \frac{12}{5} = \frac{192}{25} m^2$ .
Both the cardboards are divided into 10 pieces each.
Area of the small piece of 1st cardboard $= \frac{\frac{66}{25}}{10} = \frac{66}{250} m^2$
Area of 5 small pieces of 1st cardboard $= 5\times \frac{66}{250} = \frac{66}{50} m^2$
Area of the small piece of 2nd cardboard $= \frac{\frac{192}{25}}{10} = \frac{192}{250} m^2$
Area of 3 small pieces of 2nd cardboard $= 3\times \frac{192}{250} = \frac{576}{250} m^2$
Total area of the cardboard made from 5 small pieces of 1st cardboard and 3 small pieces of 2nd cardboard $= \frac{66}{50} +\frac{576}{250} $
$=\frac {66\times 5+576}{250}$
$= \frac{330+576}{250}$
$= \frac{906}{250}$
$= \frac{453}{125} m^2$
Total area of the cardboard made from 5 small pieces of 1st cardboard and 3 small pieces of 2nd cardboard is $\frac{453}{125} m^2$
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