Question

Area of rectangular field is3584 and length and bredth are in the ratio 7:2 resp.What is perimeter of rectangle

Answer 1

Answer:

The Perimeter of the Rectangle is 288 units.

Step-by-step explanation:

Given :

Area of the Rectangle = 3584

Ratio of length to breadth = 7 : 2

To find :

The Perimeter of the Rectangle

Solution :

Let the -

• Length be 7x
• Breadth be 2x

★$\green{\boxed{\green{\boxed{\red{\sf{Area=Length \times Breadth}}}}}}$

$\tt{\longrightarrow} \: 7x \times 2x = 3584 \\ \tt{\longrightarrow} \: {14x}^{2} = 3584 \\ \tt{\longrightarrow} \: {x}^{2} = \frac{3584}{14} \\ \tt{\longrightarrow} \: {x}^{2} = 256 \\ \tt{\longrightarrow} \: x = \sqrt{256} \\ \tt{\longrightarrow} \: x = 16$

$\rule{300}{1.5}$

★ Value of 7x

$\tt{\longrightarrow} \: 7(16) \\ \tt{\longrightarrow} \: 112$

Length = 112

$\rule{300}{1.5}$

★ Value of 2x

$\tt{\longrightarrow} \: 2(16) \\ \tt{\longrightarrow} \: 32$

Breadth = 32

• Length = 112
• Breadth = 32

$\rule{300}{1.5}$

Perimeter of the Rectangle -

$\green{\boxed{\green{\boxed{\red{\sf{Perimeter=2(Length + Breadth)}}}}}}$

$\tt{\longrightarrow} \: 2(112 + 32) \\ \tt{\longrightarrow} \:224 + 64 \\ \tt{\longrightarrow} \:288$

$\therefore$ The Perimeter of the Rectangle is 288 units.

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :}}}}$

The Perimeter of the Rectangle is 288 Units.

$\mathfrak{\large{\underline{\underline{Explanation :}}}}$

Gívєn -

Area = 3584

Ratio = 7 : 2

Tσ fínd -

Its Perimeter

Sσlutíσn -

Consider the -

• Length as 7y
• Breadth as 2y

Area = $\boxed{\sf{Length \times Breadth}}$

➠ 7y × 2y = 3584

➠ 14y² = 3584

➠ y² = 3584 ÷ 14

➠ y² = 256

➠ y = $\sqrt{256}$

➠ y = 16

Length =

➠ 7 × 16

➠ 112

Breadth =

➠ 2 × 16

➠ 32

$\rule{300}{1.5}$

Perimeter of the Rectangle -

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

➠ 2(112 + 32)

➠ 224 + 64

➠ 288

The Perimeter of the Rectangle is 288 Units.