Question

The perimeter of a rectangle is 130 cm. If the length of the rectangle is 10 cm less than twice of its breadth, find the area of the rectangle.​

Answer 1

Given

• Perimeter of a rectangle = 130 cm
• Length of the rectangle is 10 cm less than twice of its breadth.

To find

• Area of the rectangle

Solution

Let the breadth of the rectangle be x cm and the length of the rectangle be (2x - 10) cm.

Using formula,

Perimeter of the rectangle = 2(l + b)

where,

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

Substituting the given values,

⟶ 130 = 2(2x - 10 + x)

⟶ 130 = 2(3x - 10)

⟶ 130/2 = 3x - 10

⟶ 65 = 3x - 10

⟶ 65 + 10 = 3x

⟶ 75 = 3x

⟶ 75/3 = x

⟶ 25 = x

The value of x = 25

Therefore, the dimensions of the rectangle :-

• length of the rectangle = 2x - 10 = 2 × 25 - 10 = 50 - 10 = 40 cm
• Breadth of the rectangle = x = 25 cm

Using formula,

Area of the rectangle = l × b

where,

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

Substituting the values,

⟶ 25 × 40

⟶ 1000 cm²

Area of the rectangle = 1000 cm²

Answer 2

Question :-

• The perimeter of a rectangle is 130 cm. If the length of the rectangle is 10 cm less than twice of its breadth, find the area of the rectangle.

Given :-

• The length of the rectangle is 10 cm less than twice of its breadth.
• Perimeter of the Rectangle = 130cm

To Find :-

• What is the Area of the Rectangle ?

Solution :-

Let the Breadth be x cm

Then, the Length will be 2(x - 10) cm

★ Perimeter of Rectangle = 2( l + b) ★

⇛ 130 = 2( 2x - 10 + x )

⇛ 130 = 2( 3x - 10 )

⇛ 130 = 6x - 20

⇛ 130 + 20 = 6x

⇛ 150 = 6x

⇛ 150/6 = x

⇛ 25 = x

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• Breadth = x = 25cm
• Length = 2 (x - 10) = 2( 25 - 10) = 50 - 10 = 40cm

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★ Area of Rectangle = L × B ★

⇛ Area of Rectangle = 40 × 25

⇛ Area of Rectangle = 1000cm²

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So, Area of Rectangle is 1000cm²

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★ Additional Info :

• Area of Square = Side x Side
• Area of Rectangle = Length × Breadth
• Area of Triangle = ½ × base x height
• Area of parallelogram = base x height
• Area of circle = πr²
• Area of Rhombus = ½ × product of its diagonals
• Area of Trapezium = ½ × height × sum of parallel sides
• Area of Polygon = sum of the area of all regions into which it is divided

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