Question

The breadth of a rectangle is 27cm. Its perimeter is 208 cm. Find the length of the rectangle.​

Answer 1

Given

• Breadth of a rectangle = 27 cm
• Perimeter of a rectangle = 208 cm

To find

• Length of the rectangle

Concept

We are having the value of the breadth and perimeter of rectangle. Firstly, we will let the breadth as x. Then by using the formula of perimeter of rectangle, we will find the value of x. Then by substituting the value of x in the length we will get the value of length of the rectangle.

Solution

Let the length of the rectangle be x.

Using formula,

Perimeter of rectangle = 2(l + b)

where,

• l = length of the rectangle
• b = breadth of the rectangle

Substituting the values,

⟶ 208 = 2(x + 27)

⟶ 208 = 2x + 54

⟶ 208 - 54 = 2x

⟶ 154 = 2x

⟶ 154/2 = x

⟶ 77 = x

The value of x = 77

Therefore, the length of the rectangle = 77 cm

________________________________

Let's verify :-

Perimeter of the rectangle = 2(l + b)

Length of the rectangle = 77 cm

Breadth of the rectangle = 27 cm

Substituting the values in the formula,

⟶ 2(77 + 27)

⟶ 2(104)

⟶ 208 cm

Hence, verified.

Answer 2

Question :-

• The breadth of a rectangle is 27cm. Its perimeter is 208 cm. Find the length of the rectangle.

Given :-

• Breadth of the Rectangle = 27cm
• Perimeter of the Rectangle = 208cm

To Find :-

• Length of the Rectangle

Solution :-

${:} \longrightarrow \sf\boxed{\bf{Perimeter_{(Rectangle)} \: = \: 2(Length \: + \: Breadth) }}$

${:} \longrightarrow \sf{\sf{208 \: = \: 2(Length \: + \: 27) }}$

${:} \longrightarrow \sf{\sf{\cancel\dfrac{208}{2} \: = \: Length \: + \: 27 }}$

${:} \longrightarrow \sf{\sf{104\: = \: Length \: + \: 27 }}$

${:} \longrightarrow \sf{\sf{104\:- \: 27 \:= \: Length \: }}$

${:} \longrightarrow \sf{\bf{77\: = \: Length \: }}$

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Verification :-

$\longmapsto \sf\boxed{\bf{Perimeter_{(Rectangle)} \: = \: 2(Length \: + \: Breadth) }}$

$\longmapsto \sf{\sf{ 208\: = \: 2(77\: + \: 27) }}$

$\longmapsto \sf{\sf{ 208\: = \: 2\: \times \: 104 }}$

$\longmapsto \sf{\bf{ 208\: = \: 208 }}$

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$\begin{gathered}\begin{gathered} \therefore\: \sf{ Length \: of \: Rectangle\: = \underline {\underline{ 77cm}}}\\\end{gathered}\end{gathered}$

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More For Knowledge :-

• Perimeter of Parallelogram = 2(Base + Height)
• Perimeter of Triangle = Side + Side + Side
• Perimeter of Rectangle = 2(Length + Breadth)
• Perimeter of Square = 4× Side
• Perimeter of Rhombus = 4 × Side
• Perimeter of Hexagon = 6 × Side
• Perimeter of Heptagon = 7 × Side
• Perimeter of Octagon = 8 × Side

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