Question

2. A carpet of size 10 m x 2 m has a 25 cm wide blue border. The inner part of the
carpet is red in colour. What is the ratio of the area of the blue border to the red
portion?​

Answer 1

⇒ Given:

Dimensions of the carpet = 10 m x 2 m

Width of the blue border = 25 cm

⇒ To Find:

The ratio of the area of the blue border to the red portion.

⇒ Analysis:

First, we need to find the total area of the carpet and exclude the area of the red portion from it. This will give the area of both the red portion and the blue border. Then we can find the ratio of the values.

⇒ Formula to be used:

→ $\boxed{\sf{Area\:of\:a\:rectangle=length\times\:breadth}}$

⇒ Solution:

Length of the total carpet = 10 m = 1000 cm

Breadth of the total carpet = 2 m = 200 cm

Area of the total carpet = length x breadth

= 1000 x 200

= 200000 cm²

Length of the inner red portion

= Length of the total carpet - Width of the border

= 1000 - 25

= 975 cm

Breadth of the inner portion

= Breadth of the total carpet - Width of the border

= 200 - 25

= 175 cm

Area of the inner red portion = Length x breadth

= 975 x 175

= 170625 cm²

Area of the blue border

= Total area of carpet - Area of inner red portion

= 200000 - 170625

= 29375 cm²

Area of the blue border = 29375 cm²

Area of the red portion = 170625 cm²

Ratio formed:

29375 : 170625

5875 : 34125

1175 : 6825

235 : 1365

47 : 273

Hence the ratio formed is 47 : 273.