Question

A carpet is placed in a room leaving a border of 1 m wide all around the room.
If the room is 14 m long and 10 m wide, find the area uncovered by the carpet.
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Answer 1

Answer:

140m

Step-by-step explanation:

area=length*breath

so

14m*10m=140m

Answer 2

Given -

• Length of room is 14 m

• Breadth of room is 10 m

• Leaves a border of 1 m

To find -

• Area uncovered by the carpet.

Formula used -

• Area of rectangle.

Solution -

In the question, we are provided, with the length and breadth of a room, and they have told us, that a carpet is to be placed, in that room, but that carpet is Leaving, 1 m border, all around the room, so, we need to find the area of that uncovered part. For that, first we will deduct, 2m from length and breadth, both, and when we will obtain, new Length and breadth, we will find the area, that area, will be the uncovered part, of that room. Let's do it !

According to the question -

Length = 14m

Breadth = 10m

Leaves border = 1m

So -

We will deduct, 2m from length and breadth. Why 2m? because, there are 2 lengths and 2 breadths in a rectangle, 1m from 1st length and breadth, and 1m from 2nd length and breadth, Therefore, we will deduct, 2m directly. Let's do it!

$\sf \underline{new \: length} \: = 14m \: - 2m \: = 12m$

$\sf \underline{new \: breadth} \: = 10m \: - \: 2m \: = 8m$

$\therefore$ The new length and breadth is 12m and 8m

Now -

We have obtained,the new length and breadth, now, we will find the area of the carpet part, by applying, the formula of area of rectangle. Let's do it!

$\sf \underline{area \: of \: rectangle} \: = l \: \times \: b$

On substituting the values -

$\sf \: area \: = l \: \times \: b$

$\sf \: area \: = 12m \: \times \: 8m$

$\sf \: area \: = 96 \: {m}^{2}$

Now -

We will find the area of the, room, and then, we will deduct, the area of carpet, from the area of room, that will give us the area of the uncovered part. Let's do it!

$\sf Area \: = \: l \: \times \: b$

$\sf Area \: = \: 14m \times \: 10m$

$\sf Area \: = 140m^{2}$

At the end -

We will fine the area, of the uncovered part, by deducting, the area of room, from the area of carpet, that will give us the area of the uncovered part.

$\sf Area_{(of\: uncovered\: part)}\: = 140m^{2} - 96m^{2}$

$\sf Area_{(of\: uncovered\: part)} = 44m^{2}$

$\therefore$ The area of the uncovered part is 44m²

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