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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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Vishal Singh 7 years, 8 months ago
0Thank You