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The area of rectangle gets reduced …

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The area of rectangle gets reduced By 9 square units .if its length is reduced by 5 units and breath Is increased by 3 units. If we increase the length by 3 units nd breadth by 2 units,the area increases by 67 square units. Find the dimensions of the rectangle.
  • 1 answers

Sia ? 6 years, 6 months ago

Let length of given rectangle be x and breadth be y
{tex}\therefore{/tex} area of rectangle = xy
According to the first condition

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

or, xy + 3x - 5 y - 15 = xy - 9 

or, xy + 3x - 5y  - xy = 15 - 9

or, 3x - 5y = 6........(i)

According to the second condition,

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

or, xy + 2x + 3y + 6 = xy + 67

or, xy + 2x + 3y - xy = 67 - 6

or, 2x + 3y = 61 ...(ii)

Multiplying eqn. (i) by 3 and eqn. (ii) by 5 and then adding,

9x-15y = 18

10x + 15y = 305

or, 19x = 323
{tex}\therefore{/tex} {tex}x = \frac { 323 } { 19 } = 17{/tex}

Substituting this value of x in eqn. (i),

3(17)-5y = 6

51 - 5y = 6

or, 5y = 51 - 6

{tex}\therefore{/tex} y = 9

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