Originally the dimensions of a rectangle were 20cm by 23cm. When both dimensions were decreased by the same amount, the area of the rectangle decreased by 120cm². How do you find the dimensions of the new rectangle?

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Answer 1 · 2015-10-18T18:40:30

The new dimensions are:

$a=17$
$b=20$

Original area:
$S_1=20xx23=460cm^2$

New area:
$S_2=460-120=340cm^2$

$(20-x)xx(23-x)=340$

$460-20x-23x+x^2=340$

$x^2-43x+120=0$

Solving the quadratic equation:

$x_1=40$ (discharged because is higher than 20 and 23)

$x_2=3$

The new dimensions are:

$a=20-3=17$
$b=23-3=20$