Question

The Pelimeful of a rectangular field is 130m. If its length is 5m more that its bradth, find the length & breadth of the field.

Answer 1

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Answer 2

Answer:

Breadth = 30 m

Length = 35 m

Step-by-step explanation:

As per the provided information in the given question, we have :

• Perimeter = 130 m
• Length = 5 m more than its breadth

We are asked to calculate the length and the breadth of the field.

Let us suppose the breadth of the field as b and length as l. Now, according to the question,

$\longmapsto \rm { Length = 5 + Breadth}$

Substitute the variables at the place of length and the breadth.

$\longmapsto \rm { \ell = 5 + b \bf {\dots (1)}}$

In the question, we are given that the perimeter of the field is 130 m. We need to frame an equation in order to calculate the value of l and b. As we know that,

$\longmapsto \bf{ Perimeter_{(Rect.)} = 2(\ell + b)}$

Substituting the value of perimeter given in the question.

$\longmapsto \rm{130 = 2(\ell + b)}$

Now, substitute the value of l from the equation (1).

$\longmapsto \rm{130 = 2(5 + b + b)}$

Performing addition in the brackets.

$\longmapsto \rm{130 = 2(5 + 2b)}$

Transposing 2 from R.H.S to L.H.S. Its arithmetic operator will get changed.

$\longmapsto \rm{\dfrac{130}{2} = 5 + 2b}$

Dividing 130 by 2 in L.H.S.

$\longmapsto \rm{65= 5 + 2b}$

Transposing 5 from R.H.S to L.H.S, its sign will get changed.

$\longmapsto \rm{65- 5 = 2b}$

Performing subtraction in L.H.S.

$\longmapsto \rm{60 = 2b}$

Transposing 2 from R.H.S to L.H.S. Its arithmetic operator will get changed.

$\longmapsto \rm{\dfrac{60}{2} = b}$

Dividing 60 by 2.

$\longmapsto \bf{30 \; m = b}$

Henceforth , the breadth of the field is 30 m.

Now, substitute the value of b in the equation (1) to find the value of l.

$\longmapsto \rm { \ell = 5 + b \bf {\dots (1)}}$

Substitute the value of b.

$\longmapsto \rm { \ell = 5 + 30 \; m}$

Performing addition.

$\longmapsto \bf { \ell = 35 \; m}$

∴ The length and the breadth of the field is 30 m and 35 m.