Question

The length of a rectangle is 2 times its width. If the perimeter of the rectangle is 60 cm, then what is the area of the rectangle?

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Answer 1

Given -

• Perimeter of rectangle is 60cm

• Length of rectangle is 2 times it's width.

To find -

• Area of rectangle

Formulae used -

• Perimeter of rectangle = 2(l + b)

• Area of rectangle = l × b

Solution -

In the question, we are provided with the perimeter of the rectangle, and it's stated that the length of rectangle is 2 times it's width/breadth and we need to find the area of the rectangle. For that first we will name length as x and width/breadth as 2x, and then by using the formula of perimeter, we will find it's length and width/breadth, after that we will find it's area. Let's do it!

According to question -

Perimeter = 60 cm

Length = x cm

Breadth/width = 2x cm

Perimeter of rectangle = 2(l + b)

Where -

l = Length

b = breadth/width

On substituting the values -

$\sf \longrightarrow perimeter \: = 2(l \: + \: b) \\ \\ \\ \sf \longrightarrow \: 60cm \: = 2(x \: + \: 2x) \: cm \\ \\ \\ \sf \longrightarrow \: 60cm \: = 2(3x) \: cm \\ \\ \\ \sf \longrightarrow \: 60cm \: = (6x) \: cm \\ \\ \\ \sf \longrightarrow \: x \: cm \: = \cancel \dfrac{60}{6} \\ \\ \\ \sf \longrightarrow \: x \: cm \: = 10 \: cm$

Now -

We will find the length and breadth/width and after that we will find the area.

→ Length = 10cm

→ Breadth = 2x = 2 × 10cm = 20cm

At the end -

We have obtained the length and breadth/width, now we will finally find it's area.

Area of rectangle = l × b

On substituting the values -

$\sf \longrightarrow \: area \: = l \: \times \: b \\ \\ \\ \sf \longrightarrow \: area \: = \: 10cm \: \times \: 20 \: cm \\ \\ \\ \sf \longrightarrow \: area \: = 200 \: cm^{2}$

$\therefore$ The area of the rectangle is 200cm²

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Answer 2

Given :-

• Perimeter of Rectangle = 60cm
• Length of the Rectangle is 2times it's Breadth.

To Find :-

• Area of Rectangle

Solution :-

Let the Breadth be x cm

Then, Length will be 2x cm

★ Perimeter of Rectangle ★

⇒ Perimeter of Rectangle = 2( L + B )

⇒ 60 = 2( 2x + x )

⇒ 60 ÷ 2 = ( 2x + x )

⇒ 30 = 3x

⇒ 30 ÷ 3 = x

⇒ 10 = x

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★ Area of Rectangle ★

⇒ Area of Rectangle = L × B

⇒ Area of Rectangle = 2x * x

⇒ Area of Rectangle = 2 * 10 * 10

⇒ Area of Rectangle = 20 * 10

⇒ Area of Rectangle = 200cm²

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Therefore, Area of Rectangle is 200cm²

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★ Additional Info :

Formulas Related to Rectangle :-

• Perimeter of Rectangle = 2( l + b)
• Area = Length × Breadth
• Length = Area / Breadth
• Breadth = Area / Length
• Diagonal = √(l)² + (b)²

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