Question

If the ratio the length Of the rectangle is 3:4 and it's perimeter will be 360m. Then, Find the area​

Answer 1

Correct Question:

If the ratio of the length and Breadth Of an rectangle is 3:4 respectively and it's perimeter will be 360m. Then, Find the area

Answer:

Given:

• Ratio Of the length and Breadth of rectangle = 3:4
• Perimeter Of rectangle = 360m

To Find:

• Area Of Rectangle

Solution:

Let, The length Of Rectangle = 3x

And The Breadth of Rectangle = 4x

we, know that

$\underline{ \boxed{ \color{violet} \sf Perimeter \: Of \: rectangle = 2(l + b) }}$

where,

• Perimeter of Rectangle = 360m
• Length of Rectangle = 3x
• Breadth of Rectangle = 4x

So,

$\implies\color{orange} \sf 360 = 2(3x + 4x)$

$\implies\color{orange} \sf 360 = 2(7x)$

$\implies\color{orange} \sf 360 = 14x$

$\implies\color{orange} \sf x = \frac{ \cancel{360}}{ \cancel{14}} = 25.71$

$\implies\color{orange} \sf x = 25.7$

So, Length of Rectangle = 3x = 3 × 25.7 = 77.1m

And Breadth of Rectangle = 4x = 4 × 102.8m

Now, We, know that

$\underline{ \boxed{ \color{red} \sf Area \: Of \: rectangle =l \times b }}$

where,

• Length = 77.1 m
• Breadth = 102.8m

So,

$\implies\color{green} \sf Area \: Of \: rectangle =77.1 \times 102.8$

$\implies\color{green} \sf Area \: Of \: rectangle =7925.88 {m}^{2}$

Hence, The Area of Rectangle will Be 7925.88m²

Diagram:

$\setlength{\unitlength}{0.25cm}\begin{picture}(5,5)\thicklines\multiput(0,0)(24,0){2}{\line(0,1){7}}\multiput(0,0)(0,7){2}{\line(1,0){24}}\put(10,-2){\sf{102.8\ m}}\put(25,3){\sf{77.1\ m}}\end{picture}$

Answer 2

$\mathfrak{\underline{\pink{Given: }}}$

• Ratio Of the length and Breadth of rectangle = 3:4

• Perimeter Of rectangle = 360m

$\underline{\blue{To Find:}}$

• Area Of Rectangle .

$\mathfrak{\underline{\green{Solution:}}}$

Let, 

The length Of Rectangle = 3x

And The Breadth of Rectangle = 4x

we know,

$\underline{ \boxed{ \color{pink} \sf Perimeter \: Of \: rectangle = 2(l + b) }}$

where,

Perimeter of Rectangle = 360m

Length of Rectangle = 3x

Breadth of Rectangle = 4x

So,

$\implies 360 = 2(3x + 4x)$

$\implies 360 = 2(7x)$

$\implies 360 = 14x$

$\implies x = \frac{ \cancel{360}}{ \cancel{14}} =</p><p> 25.71$

$\implies x = 25.7$

So, Length of Rectangle = 3x = 3 × 25.7 = 77.1m

And Breadth of Rectangle = 4x = 4 × 102.8m

Now, 

$\underline{ \boxed{ Area \: Of \: rectangle =l \times b }}$

where,

Length = 77.1 m

Breadth = 102.8m

So,

$\implies \sf Area \: Of \: rectangle =77.1 \times 102.8$

$\implies \sf Area \: Of \: rectangle =7925.88 {m}^{2</p><p>}$

Hence,$\underline{\orange{The \:Area \:of \:Rectangle\: will \: Be\: 7925.88m^2}}$.

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