Question

a rectangular field has an area of 18432 square meters . it's width is half as long as it's length find its perimeter
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Answer 1

Answer:

$\star \: \textbf{ Perimeter = 576 \: m }$

Step-by-step explanation:

Given:-

• Area of rectangular field = 18432 sq.m
• Width = 1/2 of length.

To find:-

• Perimeter of field.

We know that,

$\star {\underline {\boxed{\bf\green{{Area}_{rectangle} = Length \times Width}}}}$

Now let's take width as x m .So,length =2x m.

$\sf Now, (2x * x)= 18432 \\\\\Rightarrow\sf 2x^2 = 18432 \\\\\Rightarrow\sf x^2 = \dfrac{18432}{2} \\\\\Rightarrow\sf x^2 = 9216 \\\\\Rightarrow\sf x =\sqrt{9216}$

$\Rightarrow\sf x$ = $\large{\boxed{\bf\pink{96\: m }}}$

$\rule{100}{2}$

$\mapsto\sf Length = 2x= 2(96)$ =$\large{\boxed{\sf\red{ 192 \: m}}}$

$\mapsto\sf Width = x$ = $\large{\boxed{\sf\blue{96 \: m }}}$

$\rule{200}{1}$

We know that,

$\star{\underline{\boxed{\bf\pink{{Perimeter}_{rectangle} = 2(length + width) }}}}$

$\Rightarrow\sf Perimeter = 2(192 + 96) \\\\\Rightarrow\sf 2(288) \: m$

$\Rightarrow\sf Perimeter$ = $\large{\boxed{\bf\blue{576 \: m}}}$

${\underline{\therefore{\rm{Perimeter \: of \: rectangular \: field = 576 \: m }}}}$

Answer 2

Answer:

576 m

Step-by-step explanation:

Let the length be 'a' m .

= > Breadth = 'a' / 2 m

Given :

Area of rectangular field = 18432 m²

= > a × a / 2 = 18432

= > a² = 2 × 18432

= > a = ± 192 m

Since side of length cannot be negative .

= > Length = 192 m

= > Breadth = 192 / 2 = 96 m

Now perimeter of rectangular field = 2 ( l + b )

Perimeter = 2 × 288 m

Perimeter = 576 m

Therefore , perimeter of rectangular field is 576 m.