Question

are the speeds
(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by
5 units and breadth is increased by 3 units. If we increase the length by 3 units and
the breadth by 2 units, the area increases by 67 square units. Find the dimensions
of the rectangle.​

Answer 1

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