1.

The perimeter of a rectangular field is 140 m. Ifthe length of the field is increased by 2 m and itsbreadth decreased by 3m, the area is decreased by66m². Find the length and breadth of the field.​

Answer»

\Large{\underline{\underline{\mathfrak{\bf{\red{Solution}}}}}}

\Large{\underline{\mathfrak{\bf{\orange{Given}}}}}

  • The perimeter of a rectangular field is 140 m
  • If the length of the field is increased by 2 m and its breadth decreased by 3m, the area is decreased by 66m².

\Large{\underline{\mathfrak{\bf{\orange{Find}}}}}

  • Length & breadth of rectangle

\Large{\underline{\underline{\mathfrak{\bf{\red{Explanation}}}}}}

\large{\underline{\tt{\:Using\:Formula}}}

★ perimeter of rectangle = 2*(Length + Breadth)

★ Area of rectangle = (Length × Breadth)

Now let,

  • Length = L m
  • Breadth = B m

A/C to question,

➥ perimeter of rectangle = 2* (L+B)

➥ 140 = 2*(L+B)

➥ L + B = 140/2

➥ L + B = 70 ------------(1)

Again, A/C to question,

  • Length be = (L + 2)m
  • Breadth = (B - 3 )m
  • Area = (LB - 66) m²

So, Area will be,

➥ Area of rectangle = (L +2)*(B-3)

➥ LB - 66 = (L+2)*(B-3)

➥ LB - 3L + 2B - 6 = LB - 66

➥ 3L - 2B = 66 - 6

➥ 3L - 2B = 60 -------------(2)

Multiply by 2 in equ(1)

➥ 2L + 2B = 140 ---------(3)

Add equ(2) & equ(3)

➥ 3L + 2L = 60 + 140

➥ 5L = 200

➥ L = 200/5

➥ L = 40

Keep value of L in equ(2),

➥ 3 * 40 - 2 * B = 60

➥ -2B = 60 - 120

➥ -2B = -60

➥ B = -60/(-2)

➥ B = 30

\Large{\underline{\mathfrak{\bf{\orange{Hence}}}}}

  • Length will be (L) = 40 m
  • Breadth will be (B) = 30 m

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