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**Hint:**We will first draw the figure of the rectangular figure and then analyze the question and we will see that the length of the tape required will be equal to the perimeter of the lid. Therefore, we will first define the perimeter and then derive the formula of the perimeter of a rectangle and then put the given values and get the answer.

**Complete step by step answer:**

We are given a rectangular box of sides 40 cm by 10 cm.

Now, we are asked to tie a tape all around it. That means we have to tie the tape on to the boundary of the given rectangle. Therefore, we need to find the perimeter of the given rectangle.

Let’s understand what basically is meant by perimeter. A perimeter means the distance of the boundary of a two-dimensional shape. Also, it is defined as the sum of the length of all the sides of the object. The algebraic sum of the length of each side is the perimeter of that shape. We have formulas available for the various shapes in geometry.

Now, to find the perimeter of a rectangle with a given length $l$ and breadth $b$ , the perimeter $P$ will be sum of all its sides that is: $P=l+l+b+b=2l+2b=2\left( l+b \right)$

Now, we have with us length as 40 cm and breadth as 10 cm, therefore the perimeter or the length of the boundary will be: $P=2\left( l+b \right)=2\left( 40+10 \right)=100\text{ cm}$ .

**Hence, the length of the tape required is 100 cm or 1 m.**

**Note:**Students may get confused between area and the perimeter. The area is basically the measurement of space enclosed by a closed geometric figure while the perimeter is the length of the boundary. Also, always mention the units in the answer. Students may make a mistake by not mentioning the units.

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