Question

The length and perimeter of a rectangular field is 10 cm and 200 cm respectively. Find the breadth and area of the field.

Answer 1

Step-by-step explanation:

Perimeter = 2(l+b)

=> 2(10+b) = 200

=> 10+b = 100

=> b = 90cm

Area = l ×b = 10×90 = 900cm^2

Answer 2

Given :

• Perimeter = 200 cm
• Length = 10 cm

To Find :

• Breadth = ?
• Area = ?

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ Formula Used :

• ${\underline{\boxed{\sf{ Perimeter {\small_{(Rectangle)}} = 2 \bigg( Length + Breadth \bigg) }}}}$

• ${\underline{\boxed{\sf{ Area {\small_{(Rectangle)}} = Length \times Breadth }}}}$

$\dag$ Calculating the Breadth :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Perimeter = 2 \bigg( Length + Breadth \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 200 = 2 \bigg( 10 + Breadth \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 200 = 20 + 2 \times Breadth } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 200 - 20 = 2 \times Breadth } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 180 = 2 \times Breadth } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{180}{2} = Breadth } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \cancel\dfrac{180}{2} = Breadth } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf{ Breadth = 90 \; cm }}}}} \; {\green{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\dag$ Calculating the Area :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Area = Length \times Breadth } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Area = 10 \times 90 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf{ Area = 900 \; {cm}^{2} }}}}} \; {\red{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Breadth of the Rectangle is 90 cm and its area is 900 cm² .

$\\ \qquad{\rule{200pt}{2pt}}$