Answer:
The Area of the poster has changed by +1.2%
The area has increased
Step-by-step explanation:
Lets take the initial length of the poster as [tex]x[/tex], and
Initial width of the poster as [tex]y[/tex].
Therefore,
Initial area of the poster = [tex]xy[/tex]
Now after the changes to length and with:
length of the poster = [tex]x-\frac{12}{100} x[/tex]
= [tex]\frac{88}{100} x[/tex]
width of the poster = [tex]y+\frac{15}{100} y[/tex]
= [tex]\frac{115}{100} y[/tex]
New Area of the poster = [tex]\frac{88}{100} x*\frac{115}{100} y[/tex]
=[tex]\frac{88*115}{100*100} *xy[/tex]
=[tex]\frac{10,120}{10,000} *xy[/tex]
=[tex]1.012*xy[/tex]
Change in Area = Area after change - Initial Area
=[tex]1.012*xy-xy[/tex]
=[tex]0.012*xy[/tex]
Percentage area change = [Change in Area / Initial Area]*100
=[tex]\frac{0.012xy}{xy} *100[/tex]
=[tex]1.2[/tex]%
The area has increased
