The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 unit and breadth is increased by 3 units. If we increase the length by 3 unit and the breadth by 2 units, the area increases by 67 square units. Find the dimension of the rectangle?
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Step-by-step explanation:
(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
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