Question

Area of a rectangular field is 3584m2 and the length and the breadth are in the ratio 7 : 2 respectively.

What is the perimeter of the rectangle?​

Answer 1

Length and Breadth of the rectangle are in the ratio 7:2

Let Length (l) be 7x and Breadth (b) be 2x

Area of rectangle = 3584 m²

Perimeter = ?

$\bold{Area \:of\: rectangle\: =\: Length\:\times\: Breadth}$

3584 = 7x × 2x

3584 = 14x²

14x² = 3584

x² = $\dfrac{3584}{14}$

x² = 256

x = √256

x = ±16

Length and Breadth can never be negative. So, we neglect them.

x = +16

Length = 7x = 7 × 16

= $\boxed{112m}$

Breadth = 2x = 2 × 16

= $\boxed{32m}$

Now

$\bold{Perimeter\: =\: 2(l + b)}$

= 2(112 + 32)

= 2 × 144

$\boxed{Perimeter \: = \: 288\:m}$

Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

The Perimeter of Rectangle is 288 m

$\textbf{\underline{\underline{Explanation :-}}}$

$\textsf{\underline{\underline{Given :}}}$

The Area of the Rectangle = 3584 m²

Ratio of Length to Breadth = 7:2

$\textsf{\underline{\underline{To find :}}}$

The Perimeter of Rectangle

$\textsf{\underline{\underline{Solution :}}}$

Consider the Length as 7x

Consider the Breadth as 2x

★ As we know :- $\boxed{\sf{Area = Length \times Breadth}}$

$\sf{\implies} \: 7x \times 2x = 3584$

$\sf{\implies} \: {14x}^{2} = 3584$

$\sf{\implies} \: {x}^{2} = \dfrac{3584}{14}$

$\sf{\implies} \: {x}^{2} = 256$

$\sf{\implies} \: x = \sqrt{256}$

$\begin{array}{r|l} 2 & 256 \\\cline{1-2} 2 & 128 \\\cline{1-2} 2 & 64 \\ \cline{1-2} 2 & 32 \\\cline{1-2} 2 & 16 \\\cline{1-2} 2 & 8 \\\cline{1-2} 2 & 4 \\\cline{1-2} 2 & 2 \\\cline{1-2} & 1\end{array}$

⟾ 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

⟾ 2 × 2 × 2 × 2

⟾ 16

$\sf{\implies} \:x = 16$

Value of 7x

$\sf{\implies} \:7 \times 16$

$\sf{\implies} \:112$

$\boxed{\sf{Length = 112 m}}$

Value of 2x

$\sf{\implies} \:2 \times 16$

$\sf{\implies} \:32$

$\boxed{\sf{Breadth = 32 m}}$

★ Perimeter of Rectangle = $\boxed{\sf{Perimeter=2(Length+Breadth)}}$

$\sf{\implies} \:2(112 + 32)$

$\sf{\implies} \:224 + 64$

$\sf{\implies} \:288$

$\boxed{\boxed{\sf{Perimeter = 288 m}}}$

$\therefore$ The Perimeter of Rectangle is 288 m