Question

The perimeter of a square is 48 m. The area of a rectangle is 4 square m less than the area of a given square. If the length of the rectangle is 14 m, then its breadth is equal to
A. 8 m
B. 9 m
C. \[10.5\] m
D. 10 m

Answer 1

Hint: First we will use the formula of the perimeter of the square is \[4a\], where \[a\] is the side of a square. Then substitute the obtained value of the side of the square in the formula of area of square \[{a^2}\], where \[a\] is the side of a square. Then we will find the area of a rectangle by using the condition that is 4 square m less than the area of given square and use the formula of area of a rectangle, \[{\text{Area of rectangle}} = {\text{Length}} \times {\text{Breadth}}\] to find the breadth.

Complete step by step answer:

First, we will use the formula of the perimeter of the square is \[4a\], where \[a\] is the side of a square. Then substitute the obtained value of the side of the square in the formula of area of square \[{a^2}\], where \[a\] is the side of a square. Then we will find the area of a rectangle by using the condition that is 4 square m less than the area of the given square and use the formula of area of the rectangle, \[{\text{Area of rectangle}} = {\text{Length}} \times {\text{Breadth}}\] to find the breadth.

Complete step by step answer:

We are given that the perimeter of a square is 48 m.

We know that the formula of the perimeter of the square is \[4a\], where \[a\] is the side of a square.

Substituting the value of perimeter of a square in the above formula, we get

\[ \Rightarrow 48 = 4a\]

Dividing the above equation by 4 on both sides, we get

\[
   \Rightarrow \dfrac{{48}}{4} = \dfrac{{4a}}{4} \\
   \Rightarrow 12 = a \\
   \Rightarrow a = 12{\text{ m}} \\
 \]

Substituting the value of\[a\] in the formula of area of square \[{a^2}\], where \[a\] is the side of a square, we get

\[ \Rightarrow {12^2} = 144{\text{ }}{{\text{m}}^2}\]

Thus, the area of the square is 144 square m.

We are given that the area of a rectangle is 4 square m less than the area of the given square, we have

\[
   \Rightarrow {\text{Area of rectangle}} = 144 - 4 \\
   \Rightarrow {\text{Area of rectangle}} = 140{\text{ sq m}} \\
 \]

Using the formula of area of rectangle, \[{\text{Area of rectangle}} = {\text{Length}} \times {\text{Breadth}}\] in the above equation, we get

\[ \Rightarrow {\text{Length}} \times {\text{Breadth}} = 140{\text{ sq m}}\]

Substituting the value of the length in the above equation, we get

\[ \Rightarrow 14 \times {\text{Breadth}} = 140{\text{ sq m}}\]

Dividing the above equation by 14 on both sides, we get

\[
   \Rightarrow \dfrac{{14 \times {\text{Breadth}}}}{{14}} = \dfrac{{140}}{{14}} \\
   \Rightarrow {\text{Breadth}} = 10{\text{ m}} \\
 \]

Hence, option D is correct.

Note: In this question, it is advisable to remember such basic formulas of perimeter and area of square and rectangle and all other shapes as it helps in solving questions and saves time. Some students find it difficult to mug up every formula but with practice, things get easier. The student may go wrong and will find the area of the rectangle or breadth of the rectangle.