Question

The length and breadth of the rectangle are in the ratio of 1:2 and its area is 512 then length and breadth are ....

Answer 1

given is the ration os length and breadth.

let the length be x and breadth be 2x

Step-by-step explanation:

area of rectangle= length x breadth

512= 2x * x

512= $2x^{2}$

$x^{2} = 256\\\sqrt{x} = \sqrt{256\\}\\x= 16$

length= x = 16

breadth = 2x= 2 *16= 32

Answer 2

Answer:

The length and breadth of a rectangle are $16$ units and $32$ units respectively.

Step-by-step explanation:

Given : The length and breadth of the rectangle are in the ratio = $1:2$

           Area of rectangle = $512$ sq.units

To find : The length and breadth of the rectangle = ?

Solution :

• It is given that the length and breadth of the rectangle are in the ratio = $1:2$

           Area of rectangle = $512$ sq.units

• We have to find the length and breadth of the rectangle.
• We know that, rectangle has four sides and the opposite sides of rectangle are parallel to each other and they are equal in length.
• Now, according to given condition, the length be $x$ and the breadth be $2x$.
• The formula for area of rectangle is given by,

     Area of rectangle = Length*Breadth  

                            $512$ = $x*2x$

                          ∴ $512=2x^{2}$

                            ∴ $x^{2}=\frac{512}{2}$

                            ∴ $x^{2} =256$

•  Taking square roots of both the sides, we get

                            ∴ $x=\sqrt{256}$

                            ∴ $x=16$ units

• ∴ The length of rectangle = $16$ units
• So, breadth of rectangle = $2x=2*16=32$ units.

• ∴ The length and breadth of a rectangle are $16$ units and $32$ units respectively.