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#