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**Hint:**In this problem the width of carpet is specified. To cover the floor of a room we need to identify which quantity is to take in consideration. To cover the floor means we need to calculate the area of the floor. This when divided with the width of carpet will give unknown length of the carpet.

Area of rectangle $ = length \times breadth$

**Complete step by step solution:**

Consider the amount length of carpet $ = x\,\,m$

First, we need to calculate the total area of the room floor.

Given, length of room $ = 20\,m$

Breadth of room $ = 12\,m$

Area of room floor

\[

= length \times breadth \\

\Rightarrow 20 \times 12 \\

\Rightarrow 240\,{m^2} \\

\]

As we know, $ 1m = 100cm$

We can further say width of carpet,

$

75cm = \dfrac{{75}}{{100}}m \\

\Rightarrow 0.75m \\

$

To cover entire area of room with carpet

Area of room = Area of carpet required to cover

$

\Rightarrow 240{m^2} = 0.75 \times x\,{m^2} \\

\Rightarrow x = \dfrac{{240}}{{0.75}}m \\

\Rightarrow x = 320m \\

$

**Therefore, the length of carpet with width 75cm required to cover the room floor is 320 m.**

**Note:**

A cuboid has six faces and each face is a rectangle. The two faces that are opposite each other are equal. Two faces of a cuboid meet each other at an edge. The edges of a cuboid meet each other at a vertex.

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