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**Hint:**Let ${P_1}$= perimeter of square and ${P_2}$= perimeter of rectangle; side of square\[S = 40\], length of rectangle$L = 10$and B be the unknown breadth of the rectangle.

Given that ${P_1} = {P_2}$. Use the formulae of perimeter: ${P_1} = 4 \times S$ and ${P_2} = 2 \times (L + B)$

Find B by solving the equation.

**Complete step by step answer:**

We are given two geometrical figures - a square and a rectangle.

Both have the same perimeter.

We are also given some of their dimensions:

Side of the square = 40 cm

Length of the rectangle = 10 cm.

We are asked to compute the missing dimension of the rectangle, namely, the breadth of the rectangle.

We know that for a square, its perimeter is the sum of all its sides.

A square has 4 sides of equal length.

This gives us the formula for the perimeter of a square.

Perimeter of a square $ = 4 \times side$

Now, a rectangle has 4 sides too. But they are of varying lengths. That is, only the opposite sides are equal.

So, if L denotes the length and B denotes the breadth of a rectangle, then its perimeter is given by the formula: Perimeter of a rectangle \[ = 2 \times (L + B)\]

Call the side of the given square as S and its perimeter as ${P_1}$.

Similarly, call the perimeter of the rectangle as ${P_2}$

Then ${P_1} = 4 \times S$ and ${P_2} = 2 \times (L + B)$

Now we have

\[S = 40\]

Therefore, \[{P_1} = 4 \times S = 4 \times 40 = 160\]

Also, $L = 10$ and $B = ?$ implies that ${P_2} = 2 \times (L + B) = 2 \times (10 + B)$

According to the given condition, the perimeter of the square = perimeter of a rectangle.

$

\Rightarrow {P_1} = {P_2} \\

\Rightarrow 160 = 2 \times (10 + B) \\

\Rightarrow 160 \div 2 = 10 + B \\

\Rightarrow 80 = 10 + B \\

\Rightarrow 80 - 10 = B \\

\Rightarrow 70 = B \\

\Rightarrow B = 70 \\

$

Hence, the breadth of the given rectangle is 70 cm.

**Note:**

You may come across questions where width is used instead of breadth. However, both mean the same.

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