Question

The the perimeter of a square is double that a rectangle if perimeter of the square is 120 metre and length and breadth of the rectangle are in the ratio 3 :2 find the breath of the rectangle.

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Perimeter of square = 120 m
• perimeter of rectangle = 2 x perimeter of square
• length : breadth = 3 : 2

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• breadth = ???

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

Perimeter of rectangle = 2 × perimeter of square

⠀⠀⠀⠀

Perimeter of rectangle = 2 × 120 m

⠀⠀⠀⠀

Perimeter of rectangle = 240 m

⠀⠀⠀⠀

• let the length and breadth be 3x and 2x

⠀⠀⠀⠀

$\sf{\red{\boxed{\bold{ perimeter = 2( length + breadth )}}}}$

⠀⠀⠀⠀

perimeter of rectangle = 2 ( 3x + 2x )

⠀⠀⠀⠀

240 = 2 × 5x

⠀⠀⠀⠀

10x = 240

⠀⠀⠀⠀

x = 240 / 10

⠀⠀⠀⠀

x = 24

⠀⠀⠀⠀

• finding value of breadth

⠀⠀⠀⠀

2x = 2 × 24 = 48 m

⠀⠀⠀⠀

$\sf{\orange{\boxed{\bold{breadth = 48m}}}}$

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Breadth of rectangle = 48 m

Answer 2

Given:

• Perimeter of Square is double than that of a Rectangle
• Perimeter of Square = 120m
• Ratio of Length and Breadth of Rectangle = 3:2

Find:

• Breadth of Rectangle

Solution:

Let, the Length of the Rectangle = 3x m

and the Breadth of the Rectangle = 2x m

Now,

In Question it is said that the perimeter of square is double the perimeter of Rectangle.

So,

♲ Perimeter of Rectangle = 2×(Perimeter of Square)

where,

• Perimeter of Square = 120m

So,

➤ Perimeter of Rectangle = 2×(Perimeter of Square)

➤ Perimeter of Rectangle = 2×(120)

➤ Perimeter of Rectangle = 240m

Therefore, Perimeter of Rectangle = 240m

____________________

Now, we know that

♲ Perimeter of Rectangle = 2(Length + Breadth)

where,

• Length = 3x m
• Breadth = 2x m
• Perimeter of Rectangle = 240m

So,

➣Perimeter of Rectangle = 2(Length + Breadth)

➣ 240 = 2(3x + 2x)

➣ 240 = 2(5x)

➣ 240/2 = 5x

➣ 120 = 5x

➣ x = 120/5 = 24m

➣ x = 24m

So, x = 24m

____________________

Now,

➨Breadth of the Rectangle = 2x = 2×24 = 48m

____________________

✮Hence, Breadth of the Rectangle = 48m