Question

a ractangular field is 60m wide while its perimeter is 320 m.if laying of grass costs ₹7.50 per square m, how much would it cost for grass to be laid on the field leaving a bare path 8m wide all round the field

Answer 1

breath the rectangular field=60m
let the length be L
therefore
perimeter=2(L+B)
320=2L+ 120
2L=200
L=100m
The length to be covered =100-8-8=86m
breadth to be covered=60-8-8=46m
the area that need to be covered=86x46
=3956m^2
the cost =7.50x 3956
=29670rs
the cost of covering the whole field is 29;670rs

Answer 2

tex]\huge{Given :-}[/tex]

A rectangular field is 60 m wide while its perimeter is 320 m.

If laying of grass costs ₹7.50 per m².

${To\: Find :-}$

How much would it cost for grass to be laid on the field leaving a bare path 8 m wide all around the field.

$\huge{Solution :-}$

First, we have to find the length of a rectangular field :

Let,

$\begin{gathered}\small \mapsto \bf Length_{(Rectangular\: Field)} =\: l\: m\\\end{gathered}$

$\huge{Given :}$

Breadth = 60 m

Perimeter = 320 m

According to the question by using the formula we get,

$\begin{gathered}\small \implies \sf\boxed{\bold{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}\\\end{gathered}$

$\begin{gathered}\implies \sf 320 =\: 2(l + 60)\\\end{gathered}$

$\begin{gathered}\implies \sf 320 =\: 2l + 120\\\end{gathered}$

$\begin{gathered}\implies \sf 320 - 120 =\: 2l\\\end{gathered}$

$\begin{gathered}\implies \sf 200 =\: 2l\\\end{gathered}$

$\begin{gathered}\implies \sf \dfrac{200}{2} =\: l\\\end{gathered}$

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

$\begin{gathered}\implies \sf\bold{l =\: 100}\\\end{gathered}$

Hence, the length of a rectangular field is 100 m .

Now, we have to find the remaining length and breadth :

$\huge{★ Remaining\: Length :}$

$\begin{gathered}\leadsto \sf Remaining\: Length =\: 100\: m - 8\: m - 8\: m\\\end{gathered}$

$\begin{gathered}\leadsto \sf\bold{Remaining\: Length =\: 84\: m}\\\end{gathered}$

$\huge{★ Remaining\: Breadth :}$

$\begin{gathered}\leadsto \sf Remaining\: Breadth =\: 60\: m - 8\: m - 8\: m\\\end{gathered} [ /tex]</p><p></p><p> </p><p> </p><p></p><p>[tex]\begin{gathered}\leadsto \sf\bold{Remaining\: Breadth =\: 44\: m}\\\end{gathered}$

Now, we have to find the area of grass field :

$\begin{gathered}\small \implies \sf\boxed{\bold{Area_{(Grass\: Field)} =\: Remaining\: Length \times Remaining\: Breadth}}\\\end{gathered}$

$\begin{gathered}\implies \sf Area_{(Grass\: Field)} =\: 84\: m \times 44\: m\\\end{gathered}$

$\begin{gathered}\implies \sf\bold{Area_{(Grass\: Field)} =\: 3696\: m^2}\\\end{gathered}$

Hence, the area of grass field is 3696 m² .

Now, we have to find the total cost :

$\huge{Given :}$

Rate per m² = ₹7.50 m²

Area of Grass Field = 3696 m²

According to the question by using the formula we get,

$\begin{gathered}\small \dashrightarrow \sf\boxed{\bold{Total\: Cost =\: Area_{(Grass\: Field)} \times Rate_{(Per\: m^2)}}}\\\end{gathered}$

$\begin{gathered}\dashrightarrow \sf Total\: Cost =\: 3696\: {\cancel{m^2}} \times ₹ 7.50\: {\cancel{m^2}}\\\end{gathered}$

$\begin{gathered}\dashrightarrow \sf Total\: Cost =\: 3696 \times ₹ 7.50\\\end{gathered}$

$\begin{gathered}\dashrightarrow \sf\bold{\underline{Total\: Cost =\: ₹ 27720}}\\\end{gathered}$

$\therefore$ The cost for grass to be laid on the field leaving a bare path 8 m wide all around the field is ₹ 27720 .