Question

If the length of rectangle is two times of it's breadth. And it's perimeter is 180' finds its dimension.

Answer 1

Answer:

Given :-

• The length of a rectangle is two times of its breadth.
• The perimeter of a rectangle is 180 cm.

To Find :-

• What is the dimensions of a rectangle.

Formula Used :-

$\clubsuit$ Perimeter of Rectangle Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}\: \: \: \bigstar$

Solution :-

$\mapsto \bf Breadth_{(Rectangle)} =\: x\: cm$

Given that :

$\leadsto$ The length of a rectangle is two times of its breadth. So,

$\mapsto \bf Length_{(Rectangle)} =\: 2x\: cm$

Given :

• Perimeter = 180 cm

According to the question by using the formula we get :

$\implies \bf Perimeter_{(Rectangle)} =\: 180$

$\implies \sf 2(2x + x) =\: 180$

$\implies \sf 4x + 2x =\: 180$

$\implies \sf 6x =\: 180$

$\implies \sf x =\: \dfrac{\cancel{180}}{\cancel{6}}$

$\implies \sf\bold{\purple{x =\: 30}}$

Hence, the required dimensions are :

☆ Breadth of Rectangle :

$\leadsto \sf Breadth_{(Rectangle)} =\: x\: cm$

$\leadsto \sf\bold{\red{Breadth_{(Rectangle)} =\: 30\: cm}}$

☆ Length of Rectangle :

$\leadsto \sf Length_{(Rectangle)} =\: 2x\: cm$

$\leadsto \sf Length_{(Rectangle)} =\: (2 \times 30)\: cm$

$\leadsto \sf\bold{\red{Length_{(Rectangle)} =\: 60\: cm}}$

$\therefore$ The length and breadth of a rectangle is 60 cm and 30 cm respectively.

Answer 2

★ Given :-

The length of rectangle is two times of it's breadth. And it's perimeter is 180

$\:$

★ To Find :-

Dimensions of the rectangle

$\:$

★ Used Formula :-

$\green⇝ \: \red {\boxed{ \bf \red{Perimeter \: of \: the \: rectangle \: is \: 2(Length + Breadth)}}}$

$\:$

★ Solution :-

The length of rectangle is two times of it's breadth

So,

• Length = 2x
• Breadth = x
• Perimeter = 180

$\color{navy}⇢ \: \bf \red{Perimeter \: of \: the \: rectangle \: = \: 2(L + B)}$

$\color{navy}{⇢} \: \: \color{black}{\bf 180\: = \: 2(2x + x)}$

$\color{navy}{⇢} \: \: \color{black}{\bf 180\: = \: 2(3x)}$

$\color{navy}{⇢} \: \: \color{black}{\bf 180\: = \: 6x}$

$\color{navy}{⇢} \: \: \color{black}{ \displaystyle \bf \cancel{ \frac{180}{6} } = x}$

$\color{navy}{⇢} \: \: \large\colorbox{orange}{x = 30}$

∴ Breadth = x = 30

∴ Length = 2x = 30×2 = 60

$\:$

★ Verification :-

$\color{navy}{⇢} \: \: \color{black}{\bf 180\: = \: 2(60+ 30)}$

$\color{navy}{⇢} \: \: \color{black}{\bf 180\: = \: 2(90)}$

$\color{navy}{⇢} \: \: \color{black}{\bf 180\: = \: 180}$

∵ Hence, verified

$\:$

The dimensions of the rectangle are :

• Length = 60
• And Breadth 30