Question

The length and breadth of a rectangular field are in ratio 9:5 if the area of field is14580 square metres, find the cost of sorrounding the field with fence at rate of rupees 3. 25 per meter
​

Answer 1

Answer

• Length : Breadth = 9:5
• Area of the rectangle = 14580 m²
• Cost of fencing per meter = ₹3.25
• Total cost for fencing the field = ?

$\displaystyle\underline{\bigstar\:\textsf{According to the given Question :}}$

• First we shall find the area of the rectangle to find the sides and then the perimeter. We shall multiply it with the cost per m² to get our Answer!!
• Assume the sides as 9x & 5x

$\displaystyle\sf :\implies Area = l \times b$

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

$\displaystyle\sf :\implies 14580 = 45x^2$

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

$\displaystyle\sf :\implies 324 = x^2$

$\displaystyle\sf :\implies \sqrt{324} = x$

$\displaystyle:\implies\underline{\boxed{\sf x = 18}}$

$\displaystyle\sf \dag \ Length = 9\times 18 = \pink{162 \ m}$

$\displaystyle\sf \dag \ Breadth = 5\times 18 = \pink{90 \ m}$

• The perimeter of the rectangle will be given by 2(l+b)
• Here we calculate the perimeter and not the area because we fence a field only at the borders of the field whereas area is about the inner surface

$\displaystyle\sf \dashrightarrow Perimeter = 2(162+90)$

$\displaystyle\sf \dashrightarrow Perimeter = 2(252)$

$\displaystyle\dashrightarrow\underline{\boxed{\sf Perimeter = 504}}$

$\displaystyle\underline{\bigstar\:\textsf{Cost of Fencing :}}$

➝ $\displaystyle\sf Cost = Perimeter \times Cost \ per \ m^2$

➝ $\displaystyle\sf Cost = 252\times 3.25$

➝ $\displaystyle\sf \underline{\boxed{\sf Cost = Rs \ 1638}}$

$\displaystyle\therefore\:\underline{\textsf{The cost of fencing the field will be \textbf{ Rs 1638}}}$