Question

Find the area of rectangle whose perimeter is 100 cm and length and breadth are in the ratio 3 : 2.

Only Moderator and Brainly stars Answers

I want Quality Answers..

Don't spam!!
​

Answer 1

GIVEN :-

Perimeter of rectangle = 100 cm

Ratio of length and breadth = 3 : 2

TO FIND :-

The Area of the rectangle

SOLUTION :-

Let the ratio constant be x. Then Length becomes " 3x " and breadth becomes " 2x "

The Perimeter of a rectangle is given by ,

$\begin{gathered} \\ \star \: \boxed{\green{\sf{Perimeter = 2 ( Length + Breadth)}}} \\ \end{gathered}$

Substituting the values we have ,

$\begin{gathered} \\ :\implies \sf \: 100 = 2(3x + 2x) \\ \\ \end{gathered}$

$\begin{gathered} \\ : \implies \sf \: 100 = 2(5x) \\ \\ \end{gathered}$

:⟹100=2(5x)

$\begin{gathered} \\ : \implies \sf \:100 = 10x \\ \\ \end{gathered}$

$\begin{gathered} \\ : \implies \boxed{\pink{\sf{x = 10}}} \\ \\ \end{gathered}$

Then the values of Length and breadth are ,

$\begin{gathered} \\ \longmapsto \sf \: length = 3x = 3(10) = 30 \: cm \\ \\ \end{gathered}$

$\begin{gathered} \\ \longmapsto \sf \: breadth = 2x = 2(10) = 20 \: cm \\ \\ \end{gathered}$

━━━━━━━━━━━━━━━━━━━━━━━━

Now , Area of rectangle is given by ;

$\begin{gathered} \\ \star \: \boxed{\blue{\sf{Area = Length \times Breadth}}} \\ \end{gathered}$

$\begin{gathered} \\ : \implies \sf \: Area = 30 \: cm \times 20 \: cm \\ \\ \end{gathered}$

$\begin{gathered} \\ : \implies \sf \: Area = (30 \times 20) \: {cm}^{2} \\ \\ \end{gathered}$

$\begin{gathered} \\ : \implies \boxed{\pink{\sf {\: Area = 600 \: cm {}^{2} }}} \: \bigstar \\ \\ \end{gathered}$

$\begin{gathered} \\ \underline{\sf{Hence\: , The\: Area\:of\:the\:rectangle\:is\: \bold{600\:cm^2}}}\end{gathered}$

Answer 2

Answer:

GIVEN :-

Perimeter of rectangle = 100 cm

Ratio of length and breadth = 3 : 2

TO FIND :-

The Area of the rectangle

SOLUTION :-

Let the ratio constant be x. Then Length becomes " 3x " and breadth becomes " 2x "

The Perimeter of a rectangle is given by ,

\begin{gathered}\begin{gathered} \\ \star \: \boxed{\green{\sf{Perimeter = 2 ( Length + Breadth)}}} \\ \end{gathered}\end{gathered}

⋆

Perimeter=2(Length+Breadth)

Substituting the values we have ,

\begin{gathered}\begin{gathered} \\ :\implies \sf \: 100 = 2(3x + 2x) \\ \\ \end{gathered}\end{gathered}

:⟹100=2(3x+2x)

\begin{gathered}\begin{gathered} \\ : \implies \sf \: 100 = 2(5x) \\ \\ \end{gathered}\end{gathered}

:⟹100=2(5x)

:⟹100=2(5x)

\begin{gathered}\begin{gathered} \\ : \implies \sf \:100 = 10x \\ \\ \end{gathered}\end{gathered}

:⟹100=10x

\begin{gathered}\begin{gathered} \\ : \implies \boxed{\pink{\sf{x = 10}}} \\ \\ \end{gathered}\end{gathered}

:⟹

x=10

Then the values of Length and breadth are ,

\begin{gathered}\begin{gathered} \\ \longmapsto \sf \: length = 3x = 3(10) = 30 \: cm \\ \\ \end{gathered}\end{gathered}

⟼length=3x=3(10)=30cm

\begin{gathered}\begin{gathered} \\ \longmapsto \sf \: breadth = 2x = 2(10) = 20 \: cm \\ \\ \end{gathered}\end{gathered}

⟼breadth=2x=2(10)=20cm

━━━━━━━━━━━━━━━━━━━━━━━━

Now , Area of rectangle is given by ;

\begin{gathered}\begin{gathered} \\ \star \: \boxed{\blue{\sf{Area = Length \times Breadth}}} \\ \end{gathered}\end{gathered}

⋆

Area=Length×Breadth

\begin{gathered}\begin{gathered} \\ : \implies \sf \: Area = 30 \: cm \times 20 \: cm \\ \\ \end{gathered}\end{gathered}

:⟹Area=30cm×20cm

\begin{gathered}\begin{gathered} \\ : \implies \sf \: Area = (30 \times 20) \: {cm}^{2} \\ \\ \end{gathered}\end{gathered}

:⟹Area=(30×20)cm

2

\begin{gathered}\begin{gathered} \\ : \implies \boxed{\pink{\sf {\: Area = 600 \: cm {}^{2} }}} \: \bigstar \\ \\ \end{gathered}\end{gathered}

:⟹

Area=600cm

2

★

\begin{gathered}\begin{gathered} \\ \underline{\sf{Hence\: , The\: Area\:of\:the\:rectangle\:is\: \bold{600\:cm^2}}}\end{gathered}\end{gathered}

Hence,TheAreaoftherectangleis600cm

2