Question

4) The perimeters of a square and
rectangle are equal. The area of the
square is 36 cm². If the length of the
rectangle is twice its breadth, what are
the dimensions of the rectangle?​

Answer 1

Explanation:

Let the length and breadth of the rectangle be 2x m and x m, respectively.

According to the question:

2x×x=288

⇒2x

2

=288

⇒x

2

=144

⇒x=12 or x=−12

⇒x=12 (∵x cannot be negative)

∴ Length =2×12=24m

Breadth=12m

Answer 2

Given :-

Perimeter of square = Perimeter of rectangle

The area of the  square = 36 cm²

The length of the  rectangle is twice its breadth.

To Find :-

The length of the rectangle.

The breadth of the rectangle.

Solution :-

We know that,

• p = Perimeter
• a = Area
• l = Length
• b = Breadth

Finding the length of the square,

Area = Length²

Length² = Area

Given that,

Area of the  square = 36 cm²

By substituting,

Length² = 36

By transposing,

Length = √36

Length = 6 cm

By the formula,

$\underline{\boxed{\sf Perimeter \ of \ a \ square=4 \times Side}}$

Given that,

Side (s) = 6 cm

Substituting their values,

p = 4 x 6

p = 24 cm

According to the question,

Perimeter of the rectangle = Perimeter of the square

Perimeter of the rectangle = 24 cm

Let the length and breadth of the rectangle be x and 2x.

By the formula,

$\underline{\boxed{\sf Perimeter \ of \ rectangle=2(Length +Breadth) }}$

Given that,

Perimeter (p) = 24 cm

Substituting their values,

24 = 2(x + 2x)

24 = 2(3x)

24 = 6x

By transposing,

x = 24/6

x = 4

Finding the dimension,

Breadth (b) = x = 4 cm

Length (l) = 2x = 8 cm

Therefore, the length and breadth of the rectangle is 8 cm and 4 cm respectively.