Question

The ratio of length and width of a rectangular field are in the ratio 3:2.The cost of fencing the field at Rs6.50 per meter is Rs520.find the dimension of the field

Answer 1

Answer:

520÷6.50=80

80 is perimeter

2(2x+3x)=80

5x=80÷2

5x=40

x=40÷5

x=8

Answer 2

Answer:

$\star\it{Reference \: of \: diagram \: given \: below:- }$

$\setlength{\unitlength}{0.78 cm}\begin{picture}(12,4)\thicklines\put(5.6,9.1){ A }\put(5.5,5.8){ B }\put(11.1,5.8){ C }\put(11.05,9.1){ D }\put(4.5,7.5){ 16\:cm }\put(8.1,5.3){ 24 \:cm }\put(11.5,7.5){ 16 \:cm }\put(8.1,9.5){ 24\:cm }\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\end{picture}$

Given:-

• Ratio of length & width = 3 : 2
• Cost of fencing @Rs.6.50 = Rs.520

To find:-

• Dimensions of field = ?

Let length and width of rectangular field be 3x & 2x m respectively.

$\rm We \: know, \\\\\star\: {\boxed{\rm{Perimeter_{rectangle} = 2(length + width) }}}$

$\twoheadrightarrow\sf Perimeter = 2(3x + 2x) \\\\\twoheadrightarrow\sf Perimeter = 2 \times 5x \\\\\twoheadrightarrow\large{\underline{\boxed{\sf\green{Perimeter = 10x \: m }}}}$

$\rule{200}{1}$

$\rm We \: also \: know \\\\\dag \: \: {\boxed{\sf\blue{Cost \: of \: fencing = Perimeter \times Rate }}}$

• Putting values:-

$\twoheadrightarrow\sf 520 = 10x \times 6.5 \\\\\twoheadrightarrow\sf 520 = 65x \\\\\twoheadrightarrow\sf x = 520/65 \\\\\twoheadrightarrow\large{\underline{\boxed{\sf\blue{x = 8 \: m }}}}$

$\rule{100}{2}$

• Now,dimensions of field:-

$\twoheadrightarrow\sf Length = 3x = 3(8) = \large{\boxed{\sf\red{24 \: m }}}$

$\twoheadrightarrow\sf Width = 2x = 2(8) = \large{\boxed{\sf\blue{16\: m }}}$