Question

The perimeter of a rectangle is 75 cm. Its
3
length is 2 times its breadth. Find the
4
length and breadth of the rectangle.
2​

Answer 1

Correct Question:

The perimeter of a rectangle is 75 cm. Its length is 2 times its breadth. Find the length and breadth of the rectangle.

Required Solution:

Given:

• Perimeter of a rectangle = 75 cm
• Length = Two times its breadth.

To calculate:

• Length and breadth of the rectangle.

Calculation:

Let the breadth of the rectangle be x.

• Therefore, its breadth becomes = 2x

We know that,

• Perimeter of the rectangle = 2 ( l + b )

|| According to the question: ||

→ 75 = 2 ( 2x + x )

→ 75 = 2 ( 3x )

→ 75 = 6x

→ x = $\sf {\cancel{ \dfrac{75}{6}} }$

→ x = 12.5 m [ Breadth ]

• Breadth = x = 12.5 cm
• Length = 2x = 2 × 12.5 = 25 cm

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Extra!!

Perimeter:

• Perimeter of square : 4 × side
• Perimeter of rectangle : 2 ( l + b )
• Perimeter of parallelogram : 2 ( l + b )
• Perimeter of rhombus : 4 × side
• Perimeter of trapezium : Sum of sides
• Perimeter of triangle : Sum of sides
• Perimeter of circle (circumference) : 2πr

Area:

• Area of square : (Side)²
• Area of rectangle : l × b
• Area of parallelogram : Base × height
• Area of rhombus : ½ × diagonal$\sf {_1}$ × diagonal$\sf {_2}$
• Area of trapezium : ½ × (sum of parallel sides) × h
• Area of triangle : ½bh
• Area of circle : πr²

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Answer 2

Let the breadth be = b

∴ Length = 2 × b {Given}

Perimeter = 75 cm

We know,

Perimeter of rectangle = 2(l + b)

∴ 2(l + b) = 75

⇒l + b = 37.5

⇒2b + b = 37.5

⇒3b = 37.5

⇒b = 12.5 cm

∴ l = 2b = 2(12.5 cm) = 25 cm

Formulae related to rectangle and cuboid:-

• Perimeter = 2(l + b)
• Area = l × b
• Diagonal of cuboid = √(l² + b² + h²)
• Volume of cuboid = l × b × h
• CSA = 2h(l + b)
• TSA = 2(lb + bh + lh)