Question

The perimeter of a rectangle is 360 cm. The length and breadth of the rectangle is in the ratio of 2 : 4. Then, find the area and the length and breadth of the rectangle.

Answer 1

Answer:

• Length of rectangle = 60 cm.
• Breadth of rectangle = 120 cm.
• Area of rectangle = 7200 cm².

Step-by-step explanation:

Given :-

• The perimeter of the rectangle is 360 cm.
• The length and the breadth of the rectangle is in the ratio of 2 : 4.

To find :-

• Length and breadth of the rectangle.
• Area of the rectangle.

Solution :-

In order to find the the area of the rectangle it is important to have it's dimensions. So, let us assume the length of the rectangle be 2x. So, the value of breadth of the rectangle will be 4x, since the ratio of length and breadth of the rectangle is 2 : 4. So, by using the formula of perimeter of rectangle we will find out dimensions.

Given :

• Length of rectangle= 2x.
• Breadth of rectangle = 4x.
• Perimeter of rectangle = 360 cm.

According to the question :

$\sf \longrightarrow {Perimeter\ of\ rectangle\ =\ 2(length\ +\ breadth)}$

• On substituting the values,

$\sf \longrightarrow {360\ =\ 2(2x\ +\ 4x)}$

$\sf \longrightarrow {360\ =\ 4x\ +\ 8x}$

$\sf \longrightarrow {360\ =\ 12x}$

$\sf \longrightarrow {\dfrac{\cancel{360}}{\cancel{12}}\ =\ x}$

$\sf \longrightarrow {30\ =\ x}$

$\sf \longrightarrow {\underline{x\ =\ 30}}\ \bigstar$

Now we have the value of x as 30. So, before proceeding to the next step, let's confirm the value of x by verifying it.

$\sf \longrightarrow {Perimeter\ of\ rectangle\ =\ 2(length\ +\ breadth)}$

$\sf \longrightarrow {360\ =\ 2(2x\ +\ 4x)}$

• Putting x = 30, we get,

$\sf \longrightarrow {360\ =\ 2(2 \times 30\ +\ 4 \times 30)}$

$\sf \longrightarrow {360\ =\ 2(60\ +\ 120)}$

$\sf \longrightarrow {360\ =\ 120\ +\ 240}$

$\sf \longrightarrow {360\ =\ 360}$

$\sf \longrightarrow {\underline{LHS\ =\ RHS}}\ \bigstar$

Now, LHS is equal to the RHS. Hence, the value of x is correct.

So, now we will find out the length and breadth of the rectangle by putting the value of x in the assumed dimensions.

• Length : 2x = 2(30) = 2 × 30 = 60 cm.
• Breadth : 4x = 4(30) = 4 × 30 = 120 cm.

Now we have the length and breadth of the rectangle. So, by using the formula of area of rectangle we will find out area.

Given :

• Length of rectangle = 60 cm.
• Breadth of rectangle = 120 cm.

According to the question :

$\sf \longrightarrow {Area\ of\ rectangle\ =\ length \times breadth}$

• On substituting the values,

$\sf \longrightarrow {60 \times 120}$

$\sf \longrightarrow {\underline{7200\ cm^2}}\ \bigstar$

∴ Hence, the area of the rectangle is 7200 cm².

Answer 2

Given :

• Perimeter of Rectangle = 360cm
• Ratio of length and breadth of the rectangle = 2:4

To Find :

• Length and Breadth of the Rectangle
• Area of the Rectangle

Solution :

✰ In this question, Perimeter of a Rectangle along with the ratios of the length and breadth are given and we have to find the measure of its length and breadth along with its area . So let's assume the length be 2p and breadth be 4p . So firstly we will find the length and breadth of the rectangle using 2(Length + Breadth) and after we will use Length × Breadth to find the area of the Rectangle.

⠀⠀⠀

⠀⠀⠀⟼⠀⠀Perimeter = 2(L + B)

⠀⠀⠀⟼⠀⠀360 = 2(2p + 4p)

⠀⠀⠀⟼⠀⠀360 = 2 × 6p

⠀⠀⠀⟼⠀⠀360/2 = 6p

⠀⠀⠀⟼⠀⠀180 = 6p

⠀⠀⠀⟼⠀⠀180/6 = p

⠀⠀⠀⟼⠀⠀30cm = p

⠀

Therefore :

➣ Length of Rectangle = 2p

➣ Length of Rectangle = 2 × 30

➣ Length of Rectangle = 60cm

⠀

➣ Breadth of Rectangle = 4p

➣ Breadth of Rectangle = 4 × 30

➣ Breadth of Rectangle = 120cm

___________________

✰ Now we have got the Length and Breadth of the Rectangle, so simply we can apply the Formula of Area of Rectangle I.e Length × Breadth .

⠀⠀⠀

⠀⠀⠀⟼⠀⠀Area = Length × Breadth

⠀⠀⠀⟼⠀⠀Area = 60 × 120

⠀⠀⠀⟼⠀⠀Area = 7200cm²

⠀⠀⠀

Thus Area of the Rectangle is 7200cm²

___________________