Question

If the perimeter of a rectangle is 40 cm. if its length is 14 cm, then find its breadth and area.

Answer 1

Answer:

Breadth is 6cm

Step-by-step explanation:

Perimeter of rectangle = 2(l+b)

40=2(14+b)

40/2 = 14+b

20 = 14+b

20-14=b

6=b

6cm = breadth

Answer 2

Given that:-

• Perimeter of Rectangle = 40cm
• Length of Rectangle = 14cm

To Attain:-

• Breadth of Rectangle
• Area of Rectangle

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A N A L Y S I S:

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In this Question, We are provided with the Perimeter and length of Rectangle and asked to find breadth and area of Rectangle. So, To find Breadth we will divide the perimeter with 2 and then subtract the result with length after that we already know that what's the Length and breadth of rectangle so, by using the Formula of area! we will find the result, so, let's find out•

☀️ D I A G R A M :

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$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large 8\ cm}\put(4.4,2){\bf\large 14\ cm}\end{picture}$

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Solution:

Perimeter of Rectangle = 40cm

Length of Rectangle = 14cm

Let the Breadth be = b

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

$:\implies \sf \: Perimeter \: of \: Rectangle \: = 40cm$

$:\implies \sf \: 2 \times (l + b) = 40cm$

$:\implies \sf \: 2 \times (14 + b) = 40cm$

$:\implies \sf \:b \: = { \cancel\dfrac{40}{2}} =20cm$

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$: \implies \sf \: Breadth = 20 - 14 = 8cm$

$\therefore \: {\underline{\sf {Hence\;,Breadth\;is\;8cm}}}$

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

Perimeter of Rectangle = 2 × (Length + Breadth)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 2 × ( 14 + 8 )

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 2 × 20

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 40cm

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Now, We have to find the area!

Area of Rectangle = Length × Breadth

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 14 × 8

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 112cm²

$\therefore \: {\underline{\sf {Hence\;,Area\;is\;112cm}^{2}}}$

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More Formulae Related to Concept:

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