Question

The ratio between length and breadth of a field is 10 : 6. The area of the field is 3840m². Find the difference between the length and width of the field.​

Answer 1

Answer:

32 m

Step-by-step explanation:

let ratio constant be x

length = 10x breadth = 6x

area= 3840 m^2

area = length * breadth

10x * 6x = 3840

60x^2 = 3840

x^2= 3840 /60 = 64

x=√64

x=8

so length = 10 x = 10*8 = 80 m

breadth= 6x = 6*8 = 48 m

difference between length and breadth = 80 - 48=32 m

Answer 2

Given :

• Ratio of Length and breadth = 10 : 6

• Area of the field = 3840 m².

To find :

Difference between the length and breadth.

Solution :

Let the length of the Rectangle be 10x and the breadth of the Rectangle be 6x.

We know the formula for area of a Rectangle i.e,

$\boxed{\bf{A = L \times B}}$

Where :

• L = Length
• B = Breadth
• A = Area

Now by using the formula for area of a Rectangle and substituting the values in it, we get :

$:\implies \bf{A = L \times B}$

$:\implies \bf{3840 = 10x \times 6x}$

$:\implies \bf{3840 = 60x^{2}}$

$:\implies \bf{\dfrac{3840}{60} = x^{2}}$

$:\implies \bf{64 = x^{2}}$

$:\implies \bf{\sqrt{64} = x}$

$:\implies \bf{8 = x}$

$\boxed{\therefore \bf{x = 8}}$

Hence the value of x is 8.

Now let's find the length and breadth of the Rectangle i.e,

• Length = 10x

==> L = 10 × 8

==> L = 80

∴ L = 80 m.

• Breadth = 6x

==> B = 6 × 8

==> B = 48

∴ B = 48 m.

Difference between the length and breadth :

==> Length - Breadth

==> 80 - 48

==> 32

∴ 32 m.

Hence the difference between the length and breadth is 32 m.