Question

the area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3units. the area is increased by 67 square units of length is increased by 3 units and the breadth is increased by 2 units find the perimeter of the rectangle

Answer 1

See the attached image file for SOLUTION

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Answer 2

Answer:

Length(x) = 17 units

Breadth(y) = 9  units

Step-by-step explanation:

We know that the area of rectangle is of the form xy where length=x and breadth=y

Now according to question,

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

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

On solving the 2 equations,we get

xy+3x-5y-15 = xy - 9

→ 3x-5y = 6 -- (iii)

→ xy+2x+3y+6 = xy + 67

 → 2x + 3y =61 (iv)

→  6x-10y = 12(v)

→  6x+9y=183(vi)

 On subtracting (vi) from (v),we get

  -19y = -171

 → y=9

On substituting y=9 in (vi),we get

6x + 81=183

→ 6x = 102   (6x+9y=183 where y=9 is substituted in this equation)

 So, x=17

Therefore,the dimensions of the rectangle are:

Length(x) = 17 units

Breadth(y) = 9  units