Question

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 a rate of 3.25 per metre.​

Answer 1

Step-by-step explanation:

9:5 means

9x × 5x = 45x'2

Area = 45x'2

14580 = 45x'2

x'2 = 324

√x'2 = √324

x = 18 m

length = 9x = 9×18 = 162 m

breadth = 5x = 5×18 = 90 m

Perimeter = 2( l+b )

2(252)

Perimeter = 504 m

504 × 3.25 = 1639 ₹

Answer 2

To find:

$\to$The cost of surrounding the field

Given:

• The length and breadth of a rectangular field are in the ratio 9 : 5

• The area of the field is 14580$m^2$

Solution:

Let,The length of the rectangular field be $\mathsf{9x}$ meter and the breadth be $\mathsf{5x}$ meter.

Here,$\mathsf{x}$ be the common multiple,

$\mathrm{Using \ formula:}$

$\to \boxed{\mathsf{Area \ of \ rectangle=Length \ * \ Breadth}}$

Now,By using the formula of area of rectangle solving the formed equation,

$\to \mathsf{9x \ * \ 5x=14580}$

$\to \mathsf{or,45x^2=14580}$

$\to \mathsf{or,x^2=\frac{14580}{45} }$

$\to \mathsf{or,x^2=324}$

$\to \mathsf{or,x=\sqrt{18 \ * \ 18}}$

$\to \mathsf{or,x=18}$

Therefore,

$\to$Length=$\mathsf{(9 \ * \ 18)m=162m}$

$\to$Breadth=$\mathsf{(5 \ * \ 18)m=90m}$

Verification:

$\to \mathsf{162 \ * \ 90=14580}$

$\to \mathsf{or,14580=14580}$

Hence,Verified (Length and Breadth)

$\mathrm{Using \ formula:}$

$\to \boxed{\mathsf{The \ perimeter \ of \ the \ rectangle = 2(Length + Breadth)}}$

By using the formula of perimeter of the rectangle finding the perimeter of the rectangle,

$\to \mathsf{2(162+90)m}\\\\\to =\mathsf{2 \ * \ 252 m}\\\\\to =\mathsf{504m}$

So,The cost of surrounding the field with a fence at the a rate of 3.25 per metre=

$\to \mathsf{(504 * 3.25)rs}\\\\\to =\mathsf{1638rs}$

Answer:

The cost of surrounding the field with a fence at the a rate of 3.25 per metre=$\mathsf{1638rs}$