Question

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. Find the length and breadth of the field.​

Answer 1

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

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

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

________________

Answer 2

$<fontcolor= blue>$

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.

$<fontcolor=black>Length & breadth of rectangle$

★ 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)

$<fontcolor=black>]Again, A/C to question,$

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)

$<fontcolor=black>Multiply by 2 in equ(1)$

➥ 2L + 2B = 140 ---------(3)

$<fontcolor=black>Add equ(2) & equ(3)$

➥ 3L + 2L = 60 + 140

➥ 5L = 200

➥ L = 200/5

➥ L = 40

$<fontcolor=black]Keep value of L in equ(2),$

➥ 3 * 40 - 2 * B = 60

➥ -2B = 60 - 120

➥ -2B = -60

➥ B = -60/(-2)

➥ B = 30

Length will be (L) = 40 m

Breadth will be (B) = 30 m