Question

A square and a rectangle have the same perimeter. If the side of the square is 16 m and the length of the rectangle is 18 m, the breadth of the rectangle is??

a. 14 m
b. 15 m
c. 16 m
d. 17 m​

Answer 1

The breadth of the rectangle is 14 m.

Step-by-step explanation

In the question, it has been stated that the perimeter of a square with side 16 m and a rectangle with length 18 m are identical. We've been asked to calculate the breadth of the rectangle.

In order to find the breadth, we must be clear with the formulas of perimeter of area and rectangle.

Perimeter

• Square · 4s units
• Rectangle · 2(l + b) units

According to the question, the perimeters of both the figures are equal, which can be written as:

$\twoheadrightarrow\quad{ \sf{4s = 2(l + b)}}$

Substituting the known values.

$\twoheadrightarrow\quad{ \sf{4 \times 16 = 2(18 + b)}}$

Multiplying the numbers in the LHS.

$\twoheadrightarrow\quad{ \sf{64 = 2(18 + b)}}$

Multiplying the expression inside the brackets with 2.

$\twoheadrightarrow\quad{ \sf{64 = 36 + 2b}}$

Transposing the like terms, i.e., moving 36 to the LHS. [In the LHS, 36 should be written as (– 36)]

$\twoheadrightarrow\quad{ \sf{64 - 36 = 2b}}$

Simplifying the LHS by subtracting 36 from 64.

$\twoheadrightarrow\quad{ \sf{28 = 2b}}$

Again transposing the like terms. This time, we will transpose 2 to the LHS. [Since 2 is multiplied in the RHS, it will be written with division symbol in the LHS]

$\twoheadrightarrow\quad{ \sf{28 \div 2 = b}}$

Writing the LHS in fractional form.

$\twoheadrightarrow\quad{ \sf{ \dfrac{28}{2} = b }}$

Reducing the fraction to its lowest form.

$\twoheadrightarrow\quad{ \sf{ \dfrac{14}{1} = b }}$

$\twoheadrightarrow\quad{ \sf{14 = b}}$

The breadth of the rectangle is 14 m. Hence, option - (a) is appropriate.