Answer:
Part a) [tex]21.9\%[/tex]
Part b) [tex]82.03\%[/tex]
Step-by-step explanation:
we know that
The original area of rectangle is equal to
[tex]A=(14)(9.5)\ cm^{2}[/tex]
so
if the length is increased by 6% and the width is by 15%
then
the new area is equal to
[tex]A=[1.06(14)][1.15(9.5)]\ cm^{2}[/tex]
[tex]A=(1.06*1.15)(14)(9.5)\ cm^{2}[/tex]
[tex]A=(1.219)(14)(9.5)\ cm^{2}[/tex]
The new area is (1.219) times the original area
Part a) Calculate the percentage change in area of the rectangle
[tex]1.219-1=0.219[/tex]
convert to percentage
[tex]0.219*100=21.9\%[/tex]
Part b) what is the original area as a percentage of the increased area of the rectangle?
Divide the original area by the increased area
[tex]\frac{(14)(9.5)}{(1.219)(14)(9.5)} =\frac{1}{1.219} \\ \\=0.8203[/tex]
Convert to percentage
[tex]0.8203*100=82.03\%[/tex]
