Question

The area of a square is 36 cm2. A rectangle has the same perimeter as the square. If the breadth of the rectangle is 4 cm, find its length.

Answer 1

$\huge{\underline{\underline{\mathtt{\orange{Given}}}}}$

The area of a square is 36 cm². A rectangle has the same perimeter as the square. If the breadth of the rectangle is 4 cm

$\huge{\underline{\underline{\mathtt{\orange{To\:find}}}}}$

Length of the rectangle

$\huge{\underline{\underline{\mathtt{\orange{Solution}}}}}$

Area of square = 36cm²

(side)² = 36

side = √36 = 6cm

Now,

Perimeter of square

= 4 × side

= 4 × 6 = 24cm

Let the length of rectangle be x

According to the given condition

Rectangle has the same perimeter as the square.

Perimeter of square = perimeter of rectangle

=> 24 = 2(l+b)

=> 24 = 2(x+4)

=> 24/2 = x+4

=> 12 = x+4

=> x = 12-4 = 8cm

$\large{\boxed{\frak{\blue{Required\:length=x=8cm}}}}$

$\huge{\underline{\underline{\mathtt{\orange{Verification}}}}}$

Perimeter of square = 24cm

Perimeter of rectangle

= 2(l+b)

= 2(8+4)= 2×12 = 24

Rectangle has the same perimeter as the square.

Hence, it is verified

$\huge\underline\frak\red{Note}$

• Perimeter of rectangle = 2(l+b)
• perimeter of square = 4×side
• Area of rectangle = l×b
• Area of square = side × side

Answer 2

Answer:

$\bold{\huge{\fbox{\color{Green}{Given}}}}$

• Area of Square = 36cm^2

• Perimeter of Square = Perimeter of Rectangle

• Breadth of Rectangle (b) = 4cm

$\bold{\huge{\fbox{\color{Green}{Find}}}}$

• Length of Rectangle = l

$\bold{\huge{\fbox{\color{Green}{Solution}}}}$

• Area of Square = a^2

• $= > {a}^{2} = 36 \\ = > a= \sqrt{36} = 6cm$
• Side of Square = 6cm

Now,

According To Question :-

• Perimeter of Sq = Perimeter of Rect.

So,

• = > 4a = 2(l + b)

• = > 4 × 6 = 2(l + 4)

• = > 24/2 = l + 4

• = > 12 - 4 = l

• = > l = 8cm

Hence,

• Length of Rectangle (l) = 8cm

More Formulas :-

=> SQUARE

• Area of Square = a^2

• Perimeter of Square = 4a

• Diagonal of Square = √2 a

=> RECTANGLE

• Area of Rectangle = l × b

• Perimeter of Rectangle = 2(l +b)

• Length of Diagonal = √(l^2 + b^2)