Question

The perimeter of a rectangular field is 240 metres. If its length is 90 m find:
i) Its Breadth
ii) Its area ​

Answer 1

Given:

• The perimeter of a rectangular field is 240m
• The Length of the rectangular field is 90m

To Find:

• The breadth of the rectangle
• The area of the rectangle

Solution:

According to the question, we have the perimeter of the rectangle and the length of the rectangle and we have to find its breadth

❍Let the breadth of the rectangle be X

As we know that,

$\: \: \: \: \star{ \blue{ \boxed{ \tt{perimeter \: of \: a \: rectangle = 2(l + b)}}}}$

Where,

• L stands for ${\bf{\pink{Length}}}$
• B stands for ${\bf{\pink{Breadth}}}$

After Substitution we get,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { : \implies} \sf \: \: perimeter = 2(l + b) \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: { : \implies} \sf240 = 2(90 + x) \\ \\ \\\: \: \: \ \: \: \: \: \: \: \: { : \implies} \sf240 = 180 + 2x \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: { : \implies} \sf2x = 240 - 180 \\ \\ \\ { : \implies} \sf2x = 60 \: \: \: \\ \\ \\ { : \implies} \sf \: x = \cancel\frac{60}{2} \\ \\ \\ \: \: { : \implies} { \boxed{\sf{ \: x = 30}}}$

• Henceforth, The breadth of the rectangle is 30m

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Now, let's find the area of the rectangle

$\underline{ \frak{As \: we \: know \: that}}$

$\: \: \: \: \: \: \star{ \pink{ { \boxed{ \tt{area _{(rectangle) } = lenght \times breadth}}}}}$

Substituting the values we get,

${ : \implies} \sf \: area \: = l \times b \: \: \: \: \\ \\ \\ { : \implies} \sf \: area = 90 \times 30 \\ \\ \\ { : \implies} \sf \: area = 2700 {m}^{2} \: \:$

• Hence the area of the rectangle is 2700m²

Diagram:

$\begin{gathered} \pink{\tt90m} \: \: \: \: \: \: \: \: \: \: \: \\ \pink{\boxed{\begin{array}{}\bf { \red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}} \pink{ \tt \:30m} \end{gathered}$

Additional Info:

★Area of a rectangle = length × breadth

★ Area of a square = side × side

★ Area of a triangle = ½ × base × hieght

★ Area of a rhombus = d₁ × d₂ / 2

★ Area of a parallelogram = base × hieght

★ Perimeter of square = 4 × side

Answer 2

Given:-

• Perimeter of Rectangular field is 240m
• Length (L) of Rectangular field is 90m

To Find:-

• Breadth (B) of Rectangular Field
• Area of Rectangular Field

Formule Used:-

• Area of Rectangle = Length × Breadth
• Perimeter of Rectangle = 2 × (L + B)

⠀⠀

D I A G R A M

$\begin{gathered}\begin{gathered} \: \: \sf 90m \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered} \: \: \: \: \: \: \: \: \boxed{\begin{array}{}\bf {\red{}}\\{\qquad \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \sf 30m\end{gathered}\end{gathered}$

⠀⠀⠀⠀

Solution with Step by step Explanation:-

Perimeter of Rectangular field = 240metres

Length of Rectangular field = 90m

Let the Breadth be = b

⠀⠀

$\: \: {\underline{\bf{\dag}\:\:{\frak{~As~we~know~that:}}}}$

⠀⠀

$\:\:\:\star\: {\boxed{\sf{\pink{~Perimeter_{(Rectangle)} = 2(\:L \:+\:B)}}}}$

⠀⠀

$\:\:\:\:{\underline{\bf{\dag}{\frak{~Substituting ~the ~Value}}}}$

⠀⠀⠀⠀

$\begin{gathered}\;\;:\implies\sf{Perimeter_{(Rectangle)} = 2(\;L\;+\;B)}\\\\\\ :\implies\sf{\; 2(\:90\;+\;b) = 240}\\\\\\ :\implies\sf{\;90\;+\:b\; } = \sf\dfrac{240 }{2} \sf \: = 120m\\\\\end{gathered}$

⠀⠀

Now,

Breadth = 120 - 90

⠀⠀⠀⠀⠀ = 30m is the Breadth

⠀⠀

V E R I F I C A T I O N

Perimeter of Rectangle = 2 ( Length + Breadth)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 2 ( 90 + 30 )

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 2 × 120

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 240m

Hence, 30 is the Breadth.

⠀⠀

______________________________________

$\: \: {\underline{\bf{\dag}\:\:{\frak{~As~we~know~that:}}}}$

⠀⠀⠀⠀

$\:\:\:\star\: {\boxed{\sf{\pink{~area_{(Rectangle)} = \:L \: \times \:B \: }}}}$

⠀⠀⠀⠀

Area of Rectangle = Length × Breadth

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 90 × 30

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 2700m²

⠀⠀⠀⠀

∴${\underline{\sf{ Hence, \: {\pmb{30m \:}} is\:Breadth\: \:and\:Area\:is\:{\pmb{2700m}^{2}} }}}$

⠀⠀⠀⠀

More Formulae Related to Concept:

• Area of Rectangle = Length × Breadth
• Perimeter of Rectangle = 2 × (L + B)
• Area of Square = Side × Side
• Perimeter of Square = 4 × Side
• Area of Parallelogram = Base × Height
• Area of Circle = $\sf{\pi r^2 }$
• Circumference of Circle = $\sf{ 2 \pi r}$
• Area of Triangle= ½ × Base × Height