Question

Exercise 18.1
1. The length and breadth of a rectangular field are in the ratio 9 : 5. If the area of the
field is 14580 square metre, find the cost of surrounding the field with a fence at the
rate of 3.25 per metre.
​

Answer 1

Answer:

ratio = 9:5

area = l*b =14580m²

let ratio = 9x:5x

AtoQ

(9x*5x)=14580

45x=14580

x=14580/45

x=324

length = 9*324 = 2916m

breadth= 5*324 = 1620m

perimeter = 2(l+b)

=2(2916+1620)

=2*4536

=9072m

cost of fencing 1m of land = 3.25rs.

cost of fencing 9072m of land = 9072*3.25

=294848 rs.

Step-by-step explanation:

hope it helps.

plz do follow me(◕ᴗ◕✿)

Answer 2

Given :

• Ratio of lenhth and breadth of a rectangular field = 9 : 5
• Area of the rectangular field = 14580 sq.m

To Find :

• The cost of surrounding the field with a fence at the rate of 3.25 per m

Solution :

Area of a rectangle is given by ,

$\\ \star \: {\boxed{\purple{\sf{Area_{(rectangle)} = length \times breadth}}}}$

We are given that ratio of length and breadth of a rectangular field as 9 : 5. Let the ratio constant be "x". Then ,

• Length = 9x
• Breadth = 5x

We are given the area of rectangular field as 14580 sq.m.

Now ,

$\\ : \implies \sf \: 14580 \: {m}^{2} = 9x \times 5x$

$\\ : \implies \sf \: 14580 \: {m}^{2} = 45 {x}^{2}$

$\\ : \implies \sf \: {x}^{2} = \frac{14580 \: {m}^{2} }{45}$

$\\ : \implies \sf \: {x}^{2} = 324 \: {m}^{2}$

$\\ : \implies \sf \: x = \sqrt{324 \: {m}^{2} }$

$\\ : \implies{\underline{\boxed {\red{\mathfrak{x = 18 \: m}}}}}$

Now ,

• Length = 9x = 9(18) = 162 m
• Breadth = 5x = 5(18) = 90 m

Perimeter of a rectangle is given by ,

$\\ \star \: {\boxed{\purple{\sf{perimeter_{(rectangle)} = 2(length + breadth)}}}}$

Substituting the values we have ,

$\\ : \implies \sf \: Perimeter_{(rectangular\:field)} = 2(162 + 90)$

$\\ : \implies \sf \:Perimeter_{(rectangular\:field)} = 2(252)$

$\\ : \implies{\underline{\boxed{\blue {\mathfrak{ Perimeter_{(rectangular \: field)} = 504 \: m}}}}} \: \bigstar$

We are given that cost of surrounding the field with fence per m as Rs. 3.25 .

Then , Cost of fencing the rectangular field per 504 m is

$\\ \longrightarrow \sf \: 504 \times 3.25 = Rs.1638$

Hence ,

• The cost of surrounding the field with fence at the rate of Rs. 3.25 per m is Rs.1638