Question

The difference between the length and the breadth of a rectangular field is 15m. If the perimeter of the field is 190m, find its length and breadth.

Answer 1

Given:-

Difference between the length and breadth of a rectangular field = 15 m

l - b = 15 m

l = 15 + b m - (i)

Perimeter of the field = 190 m

Calculation:-

Perimeter of a rectangular field = 2 * (l + b) - (ii)

190 = 2 * (l + b)

190 = 2 * (15 + b + b) [From equation (i)]

190 = 2 * (15 + 2b)

190 / 2 = 15 + 2b

95 = 15 + 2b

95 - 15 = 2b

80 = 2b

b = 80 / 2

b = 40 m

∴ Breadth = 40 m Ans.

[From equation (i)]

l = 15 + b m

l = 15 + 40 m

l = 55 m

∴ Length = 55 m Ans.

Ans.) Its length is 55 m and breadth is 40 m.

Checking:-

[From equation (ii)]

Perimeter of a rectangular field = 2 * (l + b)

= 2 * (55 + 40)

= 2 * 95

= 190 Proved.

Answer 2

Let length be l

Let breadth be b

Perimeter of rectangle is 2(l+b)

 2(l+b)=190 m

The difference between them is 15m

2(l+b)=190

l+b=95

l+b=95 → equation 1
l-b=15 → equation 2
 
2l=110

l=55 →equation 3

substitute equation 3 in equation 1

55+b=95

b=95-55

b=40

Length=55

Breadth=40