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A square and a rectangle have the same perimeter. The side of the square is 40 cm and the length of a rectangle is 10 cm, find a breadth of rectangle.
(A) 80 cm
(B) 90 cm
(C) 70 cm
(D) None

Last updated date: 13th Jun 2024
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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
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Length of the rectangle = 10 cm.
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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.

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