Question

the area of a rectangle gets reduced by 9 square metre what if its length is reduced by 5 units and breadth is increased by 3 if we increase the length by 300 and the breadth by 2 units the area increased by 67 square unit find the dimension of rectangle​

Answer 1

Let the original length be x m and breadth by y m.

Area = xy m2

(x - 5) (y + 3) = xy - 9

3x - 5y = 6 ...............(1)

(x + 3) (y + 2) = xy + 67

2x + 3y = 61 ..............(2)

Multiplying equation (1) with 2 and equation (2) with 3, we get

6x - 10y = 12 .............(3)

6x + 9y = 183 ............(4)

On subtracting (3) from (4), we get, y = 9

x = 17

Hence,

Length = 17 m

Breadth = 9 m

Answer 2

Answer:

Answer:

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Let the length of the rectangle be x m and the breadth of the rectangle be y m.

Then,

Area of rectangle = xy m²

★ If its length is reduced by 5 m and breadth is increased by 3 m,

Then,

Length = (x-5) m

Breadth = (y+3) m

A/Q, [ 1st case]

(x-5)(y+3)=xy-9

→ xy+3x-5y-15=xy-9

→ 3x-5y=15-9

→ 3x-5y = 6 .................... [ equation 1 ] ×2

★ If the length is increased by 3 m and the breadth is increased by 2 m,

Then,

Length = (x+3) m

Breadth = (y+2) m

A/Q, [ 2nd case]

(x+3)(y+2) = xy+67

→ xy +2x + 3y +6 = xy + 67

→ 2x+3y = 61................... [ equation 2] × 3

Now,

2 equations will be,

6x -10y = 12..........[1]

6x + 9y = 183.........[2]

Now subtract eq (1) from eq(2).

6x+9y-6x+10y = 183-12

→ 19y = 171

→ y = 9

Breadth = 9 m

Now out y=9 in eq(1).

3x-5y=6

→ 3x - 5×9 = 6

→ 3x = 6+45

→ x = 17

Length = 17 m