Question

The area of a rectangle is 78hole 2by 9 sq m.If its length is 10 hole 1by 3 m, then find the breadth.​
Please explain step wise​

Answer 1

D I A G R A M :

$\sf{b \:}\huge\boxed{ \begin{array}{cc} \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \sf{10 \dfrac{1}{3} \: m } \\ \\ \boxed{ \large \sf \green{Area = 78 \dfrac{2}{9} \: {m}^2}}$

$\Large {\underline { \sf \purple{Clarification :}}}$

Here we are given that the length of rectangle is $\sf { 10\dfrac{1}{3} \: m}$ and the area of the rectangle is $\sf{ 78 \dfrac{2}{9} \: {m}^2}$ . We have to find the breadth.

We'll first assume the breadth as "b".After that we'll form a linear equation. Thinking, which equation? We'll form a linear equation using the formula of the rectangle. After that, by using transposition method ; we'll find the breadth of the rectangle.

$\red \dag$ Transposition method :

• This is the method used to solve a linear equation having variables and constants.
• In this method, we transpose the values from R.H.S to L.H.S and vice-versa and changes its sign while transposing to find the value of the unknown value.

$\Large {\underline { \sf \purple{Explication \: of \: Steps :}}}$

We have,

• Length of the rectangle = $\sf { 10\dfrac{1}{3} \: m}$

• Area of the rectangle = $\sf{ 78 \dfrac{2}{9} \: {m}^2}$

Now, we have to find out breadth. Let the breadth of the rectangle be b.

As we know that,

$\bigstar \: \boxed{\sf { {Area}_{(Rectangle)} = \ell \times b}}$

• $\ell$ is length.
• b is breadth.

Substituting values,

$\longrightarrow \sf {78 \dfrac{2}{9} \: {m}^2 = 10\dfrac{1}{3} \: m \times b }$

• Transpose the value of length from R.H.S to L.H.S. As it is in the form of multiplication, so its sign will get changed and it will become in the form of division in L.H.S.

$\longrightarrow \sf { 78 \dfrac{2}{9} \: {m}^2 \div 10\dfrac{1}{3} \: m= b }$

$\longrightarrow \sf { \dfrac{704}{9} \div \dfrac{31}{3} \: {m}^{2-1} = b }$

$\longrightarrow \sf { \dfrac{704}{ \not 9} \times \dfrac{ \not 3}{31} \: m= b }$

$\longrightarrow \sf { \dfrac{704}{3} \times \dfrac{1}{31} \: m= b }$

$\longrightarrow \sf { \dfrac{704 \times 1}{3 \times 31 } \: m= b }$

$\longrightarrow \sf { \dfrac{704}{93 } \: m= b }$

$\longrightarrow \boxed {\sf { 7 \dfrac{53}{93 } \: m= Breadth }} \: \purple {\bigstar}$

$\Large {\underline { \sf \purple{ A \: Little \: Further..!}}}$

More about rectangles :

1. A rectangle is a quadrilateral having 4 sides, 4 angles and 4 vertices.
2. Opposite sides of a rectangle are parallel to each other.
3. A rectangle is a parallelogram.
4. Opposite sides of a rectangle are equal.
5. Opposite angles of a rectangle are equal.
6. All the angles of a rectangle are 90°.
7. Diagonals of a rectangle bisect each other.
8. Perimeter = 2 ( length + breadth )
9. Area = Length × Breadth