Question

Which costs more? Fencing a
rectangular field of length and breadth 18 m and 12 m,
respectively or a square field of side 30.5 m? The cost of fencing is Rs 15 per metre.
​

Answer 1

Answer:

square field costs more

Step-by-step explanation:

• rectangular field

fencing means we need to find perimeter

so perimeter = 2(l+b) m

=2(18 + 12) m

=2(30) m

= 60 m

so cost of fencing per metre is Rs 15

So cost of fencing 60m is = Rs 15*60

= Rs 900

• square field

perimeter = 4a

=4(30.5)m

= 122m

so cost of fencing 122m = Rs 15*122

= Rs 1930

• Rs 1930>Rs900
• so square field cost us more

Answer 2

Answer:

${\underline{\boxed{\sf\green{Fencing \:square \:field \:costs \:more }}}}$

Step-by-step explanation:

At first,

$\frak{Given}\begin{cases}\sf\green{Length \: of \: rectangular \: field = 18\: m}\\\sf\orange{Breadth\: of \: rectangular \: field = 12 \: m}\\\sf{Rate \: of \: fencing =Rs. 15 \: per\: m}\\\sf\blue{Cost \: of \: fencing =?}\end{cases}$

We know, fencing a field is fencing perimeter of field.

We know that,

${\underline{\boxed{\sf\blue{Perimeter \: of \: rectangle = 2(l + b) }}}}$

$\hookrightarrow\sf Perimeter \: of \: rectangular \:field = 2(18 + 12)\: m \\\\\hookrightarrow\sf Perimeter \: of \: rectangular \: field =( 2 \times 30)\: m \\\\\hookrightarrow{\boxed{\sf\blue{Perimeter \: of \: rectangular \: field = 60 \: m}}}$

$\rule{100}{2}$

$\sf Cost \: of \: fencing = Rate \times Perimeter \\\\\hookrightarrow\sf Cost \: of \: fencing = Rs.(15 \times 60) \\\\\hookrightarrow{\boxed{\sf\blue{Cost \: of \: fencing = Rs.900 }}}$

$\rule{300}{1}$

$\frak{Given}\begin{cases}\sf\green{Side \: of \: square = 30.5 \: m}\\\sf\blue{Rate = Rs.15 \: per \:m}\\\sf\purple{Cost \: of \: fencing =?}\end{cases}$

We know that,

${\underline{\boxed{\sf\purple{Perimeter \: of \: square = 4 \times Side}}}}$

$\hookrightarrow\sf Perimeter \: of \: square \: field =( 4 \times 30.5)\: m \\\\\hookrightarrow{\boxed{\sf\purple{Perimeter\: of \: square \: field = 122 \: m}}}$

$\rule{100}{2}$

$\sf Cost \: of \: fencing = Rate \times Perimeter \\\\\hookrightarrow\sf Cost \: of \: fencing = Rs.(15 \times 122) \\\\\hookrightarrow{\boxed{\sf\purple{Cost \: of \: fencing = Rs.1830}}}$

$\rule{200}{1}$

$\because\sf\green{Rs.1830 \: \: > \: \: Rs.900}$

$\therefore\sf\blue{Fencing \: square \: field \: costs \: more.}$