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 rate of
per metre.
3.25
2. Aroot
of the caure whose area equals the area of the​

Answer 1

Diagram:

$\setlength{\unitlength}{0.25cm}\begin{picture}(5,5)\thicklines\multiput(0,0)(24,0){2}{\line(0,1){7}}\multiput(0,0)(0,7){2}{\line(1,0){24}}\put(10,-2){\sf{5x\ cm}}\put(25,3){\sf{9x\ cm}}\end{picture}$

Given:

• Length and Breadth of Rectangle are in ratio 9:5
• Area of the field = 14580m²

Find:

• Cost of fencing the field's sorroundig at the rate of rs.3.25/m

Solution:

Let, Length of Rectangular field = 9x m

and Breadth of Rectangular field = 5x m

$\bold{ACCORDING \: TO \: QUESTION}$

$\sf :\implies Area \: of \: rectangle = l \times b$

$\sf :\implies 14580 = 9x \times 5x$

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

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

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

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

$\sf :\implies x = \sqrt{324} = 18m$

$\sf :\implies x = 18m$

Length = 9x = 9×18 = 162m

Breadth = 5x = 5×18 = 90m

$\sf := Perimeter \: of \: rectangle = 2(l + b)$

$\sf := Perimeter \: of \: rectangle = 2(162 + 90)$

$\sf := Perimeter \: of \: rectangle = 2(252)$

$\sf := Perimeter \: of \: rectangle = 504m$

Therefore,

Cost of fencing = 504×3.25 = 1638 Rs.

Answer 2

Let the length of rectangle be 9x and its breadth be 5x

So,

Area = l × b

⇒ 14580 = 9x × 5x

45x2 = 14580

x2 = 14580/45 = 324

x = √324

x = 18

Hence,

Length = 9 × 18 = 162 m and Breadth = 5 × 18 = 90 m

Now, Perimeter = 2(l + b)

= 2 (162 + 90) = 2(252)

= 504 m.

Therefore, cost for fencing the surrounding 504 m at the rate of ₹3.25 per metre = ₹(504 × 3.25) = ₹1638

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