Question

Find the breadth of a rectangle whose length is double of its breadth and perimeter is 720m.

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Answer 1

Given : The length is double of its breadth and perimeter is 720 m.

To Find : Breadth of Rectangle ?

_____________________

❍ Let's consider the Breadth of Rectangle be x m

$~~$

Given that,

• The length is double of its breadth.

$~~~~$$\therefore$ The Length of Rectangle is 2x m.

$~$

$\underline{\frak{As~we~know~that~:}}$

• $\boxed{\sf\pink{Perimeter_{(Rectangle)}~=~2(l~+~b)}}$

$~$

Solution : Here l is the Length of Rectangle in metres and b is the Breadth of Rectangle in metres and we have given with the Perimeter of Rectangle is 720 m.

$~$

$\underline{\bf{Now~By~Substituting~the~Given~Values~:}}$

$~$

$~~~~~~~~~~:\implies{\sf{720~m~=~2(x~+~2x)}}$

$~~~~~~~~~~:\implies{\sf{\dfrac{720}{2}~=~x~+~2x}}$

$~~~~~~~~~~:\implies{\sf{360~=~x~+~2x}}$

$~~~~~~~~~~:\implies{\sf{360~=~3x}}$

$~~~~~~~~~~:\implies{\sf{\dfrac{360}{3}~=~x}}$

$~~~~~~~~~~:\implies{\underline{\boxed{\frak{\pink{x~=~120~m}}}}}$★

$~$

Therefore,

• Length of Rectangle is 2x = 2x 120 = 240 m

• Breadth of Rectangle is x = 120 m

$~$

Hence,

$\therefore\underline{\sf{Breadth~of~Rectangle~is~120~m}}$

$~$

_______________________________________

V E R I F I C A T I O N :

$~$

• $\boxed{\sf\pink{Perimeter_{(Rectangle)}~=~2(l~+~b)}}$★

$~$

Here l is the Length of Rectangle in metres and b is the Breadth of Rectangle in metres and we have given with the Perimeter of Rectangle is 720 m.

$\underline{\bf{Now ~By~ Substituting ~the ~Found ~Values~:}}$

$~$

$~~~~~~~~~~:\implies{\rm{720~m~=~2(120~+~240)}}$

$~~~~~~~~~~:\implies{\rm{720~m~=~2(360)}}$

$~~~~~~~~~~:\implies{\rm{720~m~=~720~m}}$

$~~~~$$\qquad\quad\therefore{\underline{\textbf{\textsf{Hence Verified!}}}}$

Answer 2

Step-by-step explanation:

Given : The length is double of its breadth and perimeter is 720 m.

To Find : Breadth of Rectangle ?

_____________________

❍ Let's consider the Breadth of Rectangle be x m

~~

Given that,

The length is double of its breadth.

~~~~ \therefore∴ The Length of Rectangle is 2x m.

~

\underline{\frak{As~we~know~that~:}}

As we know that :

\boxed{\sf\pink{Perimeter_{(Rectangle)}~=~2(l~+~b)}}

Perimeter

(Rectangle)

= 2(l + b)

~

Solution : Here l is the Length of Rectangle in metres and b is the Breadth of Rectangle in metres and we have given with the Perimeter of Rectangle is 720 m.

~

\underline{\bf{Now~By~Substituting~the~Given~Values~:}}

Now By Substituting the Given Values :

~

~~~~~~~~~~:\implies{\sf{720~m~=~2(x~+~2x)}} :⟹720 m = 2(x + 2x)

~~~~~~~~~~:\implies{\sf{\dfrac{720}{2}~=~x~+~2x}} :⟹

2

720

= x + 2x

~~~~~~~~~~:\implies{\sf{360~=~x~+~2x}} :⟹360 = x + 2x

~~~~~~~~~~:\implies{\sf{360~=~3x}} :⟹360 = 3x

~~~~~~~~~~:\implies{\sf{\dfrac{360}{3}~=~x}} :⟹

3

360

= x

~~~~~~~~~~:\implies{\underline{\boxed{\frak{\pink{x~=~120~m}}}}} :⟹

x = 120 m

★

~

Therefore,

Length of Rectangle is 2x = 2x 120 = 240 m

Breadth of Rectangle is x = 120 m

~

Hence,

\therefore\underline{\sf{Breadth~of~Rectangle~is~120~m}}∴

Breadth of Rectangle is 120 m

~

_______________________________________

V E R I F I C A T I O N :

~

\boxed{\sf\pink{Perimeter_{(Rectangle)}~=~2(l~+~b)}}

Perimeter

(Rectangle)

= 2(l + b)

★

~

Here l is the Length of Rectangle in metres and b is the Breadth of Rectangle in metres and we have given with the Perimeter of Rectangle is 720 m.

\begin{gathered}\\\end{gathered}

\underline{\bf{Now ~By~ Substituting ~the ~Found ~Values~:}}

Now By Substituting the Found Values :

~

~~~~~~~~~~:\implies{\rm{720~m~=~2(120~+~240)}} :⟹720 m = 2(120 + 240)

~~~~~~~~~~:\implies{\rm{720~m~=~2(360)}} :⟹720 m = 2(360)

~~~~~~~~~~:\implies{\rm{720~m~=~720~m}} :⟹720 m = 720 m

~~~~ \qquad\quad\therefore{\underline{\textbf{\textsf{Hence Verified!}}}}∴

Hence Verified!

$\huge{\underline{\mathfrak{DISHA}}}$