Question

the length and breadth of a cardboard are two whole 1 by 5 and 1 whole 1 by 5 respectively the length and breadth of a second convert 3 whole 1 by 5 metre and 2 whole 2 by 5 respectively both carboards are divided into 10 equal small pieces what is the total area of a cardboard if it is made using 5 smaller pieces from the first cardboard and three smaller pieces from the second cardboard​

Answer 1

Given:

The dimensions of the first cardboard:

Length = $2\frac{1}{5}\: m = \frac{11}{5} \:m$

Breadth = $1\frac{1}{5}\: m = \frac{6}{5} \:m$

The dimensions of the second cardboard:

Length = $3\frac{1}{5}\: m = \frac{16}{5} \:m$

Breadth = $2\frac{2}{5}\: m = \frac{12}{5} \:m$

Both the cardboards are divided into 10 equal small pieces

To find:

The total area of cardboard if it is made using 5 smaller pieces from the first cardboard and three smaller pieces from the second cardboard​

Solution:

Here we are two cardboards and both of them are divided into 10 equal pieces, therefore, we will first calculate the area of each piece obtained by dividing the two cardboards into 10 pieces.

First Cardboard:

∴ Area of each small piece is,

= $\frac{Area\: of\: the\: first\:rectangular \:board}{10}$

= $\frac{\frac{11}{5}\times \frac{6}{5} }{10}$

= $\frac{\frac{66}{25} }{10}$

= $\frac{66}{250}$

= $0.264\:m^2$

Second Cardboard:

∴ Area of each small piece is,

= $\frac{Area\: of\: the\: second\:rectangular \:board}{10}$

= $\frac{\frac{16}{5}\times \frac{12}{5} }{10}$

= $\frac{\frac{192}{25} }{10}$

= $\frac{192}{250}$

= $0.768\:m^2$

Also, it is given that new cardboard is formed by using 5 pieces from the 1st and 3 pieces from the 2nd cardboard, so:

Area of 5 small pieces of the first cardboard = 5 × 0.264 m² = 1.32 m²

and

Area of 3 small pieces of the second cardboard = 3 × 0.768 m² = 2.304 m²

Now,

Total Area is,

= [Area of 5 small pieces of the first cardboard] + [Area of 3 small pieces of the second cardboard]

= [1.32 m²] + [2.304 m²]

= 3.624 m²

Thus, the total area of cardboard if it is made using 5 smaller pieces from the first cardboard and three smaller pieces from the second cardboard​ is 3.624 m².

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