Answer: 12.32%
Step-by-step explanation:
1. [tex]x[/tex] is the original long side and [tex]y[/tex] is the original short side.
2. The area of the original rectangle is [tex]xy[/tex].
3. The rectangle is extended 4% on the long sides and 8% on the short sides. therefore, the new long side is:
[tex]\frac{104}{100}x=\frac{26}{25}x[/tex]
4. And the new short side is:
[tex]\frac{108}{100}y=\frac{27}{25}y[/tex]
5. The new area is:
[tex](\frac{26}{25}x)(\frac{27}{25}y)=\frac{702}{625}xy[/tex]
6. The percentage of increase is calculated by substracting the new area and the original area:
[tex]\frac{702}{625}xy-xy=0.1232xy[/tex]
7. The result is:
(0.1232)(100)=12.32%