Question

length of rectangle is 2 times its width perimeter of a triangle is 180 cm find the dimensions of rectangle​

Answer 1

Question :

The Length of a Rectangle is 2 times of it's width.

If the Perimeter of the Rectangle is 180 cm. Then find the dimensions of the Rectangle.

To Find :

The Length and Width of the Rectangle .

Given :

• Perimeter of the Rectangle = 180 cm

We Know :

Perimeter of a Rectangle :

$\blue{\sf{\underline{\boxed{P = 2(Length + Breadth)}}}}$

Concept :

According to the question , the length is twice of it's Breadth.

So , let the Breadth be a , then the Length is 2a.

Hence , the length of the Rectangle is 2a and it's width is a.

Solution :

Given :

• Lenth = 2a

• Breadth = a

• Perimeter = 180 cm

Using the formula and substituting the values in it , we get :

$\large\green{\sf{P = 2(Length + Breadth)}} \\ \\ \\ \implies \sf{180 = 2(2a + a)} \\ \\ \\ \implies \sf{180 = 2 \times 3a} \\ \\ \\ \implies \sf{180 = 6a} \\ \\ \\ \implies \sf{\dfrac{180}{6} = a} \\ \\ \\ \implies \sf{30 cm = a} \\ \\ \\ \therefore \purple{\sf{a = 30 cm}}$

Hence , the value of a is 30 cm.

Since we have Taken breadth of the Rectangle as a , thus the breadth of the Rectangle is also 30 cm.

A/C , The Length of the Rectangle is twice of it's Breadth , thus the length is (2 × 30) cm , i.e 60 cm.

Hence , the length of the Rectangle is 60 cm.

Answer 2

$\underbrace{ \boxed{ \tt \red {Correct \: Question}}}$

The Length of a rectangle is two times its width. The perimeter of the rectangle is 180cm. Find the dimensions of rectangle.

$\underbrace{ \boxed{ \tt \pink S \gray ol \blue ut \red io \purple n}}$

Let the width of the rectangle be x.

It is given that the length of the rectangle is twice its width, so the length is 2x.

Now,

We know that the perimeter of a rectangle is twice the sum of its length and width.

The perimeter is given as 180 cm.

So, Perimeter of rectangle = 2(L+B)

$\implies \red{ \tt 180cm = 2(2 x+ x)}$

$\implies \blue{ \tt 180cm = 4 x+ 2x}$

$\implies \purple{ \tt 180cm = 6x}$

$\implies \pink{ \tt \frac{ \cancel{180}}{ \cancel6} = x}$

$\implies \gray{ \tt x = 30cm}$

$\tt So, the \: width \: of \: rectangle \: is \\ \tt x = 30cm \: and \: the \: length \: of \: rectangle \\ \tt is \: 2x = 2 \times 30 = 60cm.$

$\huge \tt Hence, \: dimensions \\ \huge \tt of \: rectangle \: is \\ \huge \boxed{ \tt30 \times 60}$