Question

the length and breadth of a rectangular piece of land or in the ratio 5.2 if the total cost of fencing it at rupees to 25000 find the length and breadth

Answer 1

${ \large{ \sf{CorrEct \: QuesTion :}}}$

The length and the breadth of a rectangular piece of land are in the ratio 5:2.If the total cost of fencing it at rs.12.5per meter is rs.25000, find its length and breadth.

${ \large{ \sf{AnswEr :}}}$

⠀⠀⠀☆ Length = 714.29 m

⠀⠀⠀☆ Breadth = 285.71 m

Given :

⠀☯ Ratio of length to breadth = 5 : 2

⠀☯ Total cost per meter = Rs 12.5

⠀☯ Total cost of fencing = Rs 25000. ⠀⠀⠀⠀⠀⠀⠀= Rs 25000/12.5m

⠀⠀⠀⠀⠀⠀⠀= Rs 25000/12.5m

⠀⠀⠀⠀⠀⠀⠀= 2000 m

⠀⠀$\rule{160}3$

Now,

Let us assume that the length be 5x and breadth be 2x.

☢ ${ \underline{ \boldsymbol{According \: to \: the \: question, }}}$

$:\implies\sf \: \: \: 2( 5x +2x) = 2000\\ \\ \\ \\ :\implies\sf \: \: \:2(7x) = 2000\\ \\ \\ \\:\implies\sf \: \: \:7x = \dfrac{2000}{2}\\ \\ \\ \\:\implies\sf \: \: \:7x = 1000\\ \\ \\ \\:\implies\sf \: \: \:x = \dfrac{1000}{7}$

⠀⠀$\rule{160}3$

Now, as per our assumption,

$:\implies\sf \: \: \: Length = 5x\\ \\ \\ \\ :\implies\sf \: \: \:Length = 5 \times \dfrac{1000}{7}\\ \\ \\ \\ :\implies\sf \: \: \:Length = \dfrac{5000}{7}\\ \\ \\ \\:\implies\sf \: \: \:Length={ \underline{ \boxed{ \purple{ \boldsymbol{ 714.29m}}}}} \: \bigstar$

⠀⠀$\rule{160}3$

Also,

$:\implies\sf \: \: \: breadth = 2x \\ \\ \\ \\ :\implies\sf \: \: \: breadth= 2 \times \dfrac{1000}{7} \\ \\ \\ \\ :\implies\sf \: \: \:breadth = \dfrac{2000}{7}\\ \\ \\ \\ :\implies\sf \: \: \:breadth={ \underline{ \boxed{ \blue{ \boldsymbol{ 285.71m}}}}} \: \bigstar$

⠀

⠀⠀⠀⠀⠀⠀⠀

${\therefore{\underline{\sf{Length \: and \: breadth \: are \:{\boldsymbol{714.29}} m \: and \: {\boldsymbol{285.71}} m.}}}}$

Answer 2

$\huge \pink{\bf AnSwer }$

Length and the breadth of a rectangle are of the ratio 5:3

Cost of fencing is ₹24 per m

Total cost = 9000

Length & Breadth of the rectangle

Solution

Let,

Length = 5x

Breadth = 3x

✭ Perimeter

→ Perimeter = Total Cost/Cost per m

→ Perimeter = 9000/24

→ Perimeter = 400 m

✭ Finding x

→ Perimeter = 2(l+b)

→ 400 = 2(5x+3x)

→ 400/2 = 8x

→ 200 = 8x

→ 200/8 = x

→ x = 25

✭ Length and Breadth

→ Length = 5x = 5×25 = 125 m

→ Breadth = 3x = 3×25 = 75 m