Question

the length and the breathe of a rectangular field are in ratio 5:4,if its perimeter is 108m,find the dimension of the field ​

Answer 1

Answer:

The length and breathe of the rectangle are 54cm and 24 cm respectively

Answer 2

Given :-

Ratio of the length and breadth of a rectangular field = 5 : 4

Perimeter of the rectangle = 108 m

To Find :-

The length of the rectangle.

The breadth of the rectangle.

Analysis :-

Consider the common ratio as a variable.

Multiply each side to the variable.

Make an equation accordingly and find the value of the variable.

Substitute the value of the variable in the length and breadth and find it's value too.

Solution :-

We know that,

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

Let us consider the common ratio as 'x'. Then the length and breadth would be 5x and 4x respectively.

By the formula,

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

Given that,

Perimeter (p) = 108 m

Length (l) = 5x

Breadth (b) = 4x

Substituting their values,

108 = 2(5x + 4x)

108 = 2(9x)

108 = 18x

x = 108/18

x = 6

Hence, the value of x is 6.

Therefore,

Length (l) = 5x

= 5 × 6 = 30 m

Breadth (b) = 4x

= 4 × 6 = 24 m

Therefore, the dimension of the field is 30 × 24 m.