The perimeters of a rectangle and a square are equal. If the side of the square is $6 c m$ and length of the rectangle is $4 c m$ , find the breadth of the rectangle.

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Solution

Perimeter is the sum of all four sides.
Let the length of a rectangle be denoted by $l$ and breadth by $b$ .
So perimeter of rectangle $= l + l + b + b$
$= 2 l + 2 b$ .
Perimeter of a square $= 4 \times s i d e$
It is given that, the perimeters of a rectangle and a square are equal.
Perimeter of a rectangle $=$ Perimeter of a square.
$2 l + 2 b = 4 \times s i d e$ ………………..(1)
The side of the square is $6 c m$ and length of the rectangle is $4 c m$ .
Substituting the values in equation (1),
$2 l + 2 b = 4 \times s i d e$
$(2 \times 4) + 2 b = 4 \times 6$
$8 + 2 b = 24$
Subtracting $8$ from both the sides,
$8 - 8 + 2 b = 24 - 8$
$0 + 2 b = 16$
Therefore, $2 b = 16$
Dividing $2$ from both sides,
$\frac{2 b}{2} = \frac{16}{2}$
$b = 8 c m$ .
Hence, the breadth of the rectangle is $8 c m$ .

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The perimeters of a rectangle and a square are equal. If the side of the square is 6cm and length of the rectangle is 4cm, find the breadth of the rectangle.

The perimeters of a rectangle and a square are equal. If the side of the square is $6 c m$ and length of the rectangle is $4 c m$ , find the breadth of the rectangle.