Rectangles - sides

One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm2.

What are the dimensions of the original rectangle?

Result

a =  19.25 cm
b =  9.25 cm

Solution:

$a= 10 + b \ \\ (a - 6)(b+14) = ab + 130 \ \\ ab-6 b +14 a - 6\cdot 14 = ab + 130 \ \\ 14 a - 6 b = 214 \ \\ 14 a - 6 (a-10) = 214 \ \\ 8 a = 154 \ \\ a = 19.25 \ \text{cm}$
$b = a - 10 = 9.25 \ \text{cm}$

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