Question

3. The length and breadth of a rectangular field are in the ratio
3:2. If the area of the field is 294 m², find the cost of fencing the field at 8 per metre.​

Answer 1

$\Large\mathfrak{\red{Diagram:-}}$

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$\LARGE\mathfrak{\pink{Solution:-}}$

$\large\mathbb{\orange{GIVEN:-}}$

• The length and breadth of a rectangular field are in the ratio 3:2. If the area of the field is 294 m².
• Area of the field is 294 m².

$\large\mathbb{\purple{TO FIND:-}}$

The cost of fencing the field at 8 per metre.

$\large\mathbb{\green{FORMULA:-}}$

Area of a rectangle = Length × Breadth .

Perimeter of a rectangle = 2(Length + Breadth) .

$\large\mathbb{\blue{ASSUMPTION:-}}$

Let, the Length of the rectangle be 3x

$\therefore$ the Breadth of the rectangle is 2x.

$\large\mathbb{\red{ACCORDING \:TO\: THE\: QUESTION:-}}$

$Area = Length \times Breadth \\ \\ \implies \: 294 = 3x \: \times \: 2x\\ \\ \implies \: 294 = {6x}^{2} \\ \\ \implies \: {x}^{2} = \cancel\frac{294}{6} \\ \\ \implies \: {x}^{2} = 49\\ \\ \implies \: {x} = 49\\ \\ \implies \: {x} = 7 \: m$

So, Length = 3x = (3 × 7) m = 21 m

and Breadth = 2x = (2 × 7) m = 14 m .

$Perimeter = 2(Length + Breadth) \\ \\ \implies \: Perimeter \: = 2(21 + 14)\\ \\ \implies \: Perimeter \: =2(35)\\ \\ \implies \: Perimeter \: =70 \: m$

Cost of 1 metre of fencing = ₹8

So, Cost of 70 metres of fencing = ₹ (8 × 70) = ₹560

$\large\mathbb{\purple{ANSWER:-}}$

$\implies \boxed{Rupees \:560}$

$\large\mathbb{\pink{FOCUS\: ZONE:-}}$

• Both Length and Breadth will be in same unit , i. e. , in metre.
• Fencing will be perimeter as fencing will cover the surface of the rectangle.