Question

The area of a square is

$\frac{4}{3}$


that of a rectangle. If area of square is 1024 sq. cm. and breadth of the

rectangle is 12 cm. then what is the difference between length of the rectangle and side of the

square ?​

Answer 1

Answer:

Required difference between the length of the rectangle and side of the  square is 32 cm

Step-by-step explanation:

It is given that the area of square is 1024 cm^2 and breadth of the rectangle is 12 cm. Let, length of the rectangle be a cm.

From the properties of square & rectangle: -

• Area of square = side^2
• Area o rectangle = length x breadth

= > Area of square = side^2

= > Area of square = ( length of side )^2

= > 1024 cm^2 = ( side )^2

= > ±√1024 cm^2 = side

= > ± 32 cm = side

Since length of any object can't be negative, length of side of square is 32 cm.

According to the given question, area of square is 4 / 3 of area of rectangle.

= > Area of square = 4 / 3 x area of rectangle

= > 1024 cm^2 = 4 / 3 x length x breadth

= > 1024 cm^2 = 4 / 3 x a cm x 12 cm    { since breadth of rectangle is 12 cm and length is a cm }

= > 1024 cm^2 = 4 / 3 x 12 cm x a cm

= > 1024 cm^2 = 4 x 4 x a cm^2

= > 1024 cm^2 / ( 4 x 4 cm^2 ) = a

= > 64 = a

Hence the required length of rectangle is 64 cm.

We have to find the difference between the length of the rectangle and side of the square.

Thus,

= > Required difference = Length rectangle - side of square

                            ⇒ 64 cm - 32 cm

                            ⇒ 32 cm

Hence the required difference between the length of the rectangle and side of the  square is 32 cm.

Answer 2

Answer:

The difference is 32 cm.

Step-by-step explanation:

Given that,

Area of square is 4/3 that of area of rectangle. Area of square is 1024 cm² and breadth of rectangle is 12 cm.

Let the length of the rectangle be x cm.

We know that ;

Area of square = (side)²

⇒ (side)² = 1024 cm²

⇒ side = ±√1024

⇒ side = 32 cm

∴ Side of square is 32 cm.

Area of square = $\dfrac{4}{3}$ * Area of rectangle

⇒ 1024 cm² = $\dfrac{4}{3}$ * length * breadth

⇒ 1024 = $\dfrac{4}{3}$ * x * 12

⇒ 1024 = 16 * x

⇒ x = $\dfrac{1024}{16}$

⇒ x = 64 cm

Hence, the length of the rectangle is 64 cm.

We have to find the difference between the length of the rectangle and side of the square.

Difference = length of rectangle - side of square

                 = ( 64 - 32 ) cm

                 = 32 cm

Hence, the difference is 32 cm.