Answer:
2 and 7.3
Step-by-step explanation:
[tex]P=2x+2y=18.6[/tex]
[tex]2x=18.6-2y\\x=9.3-y[/tex]
We'll replace x with (9.3-y)
[tex]A=x\cdot y=14.6\\(9.3-y)\cdot y=14.6\\-y^2+9.3y=14.6\\ \\y^2-9.3+14.6=0[/tex]
Now we solve this equation by sum and product:
[tex]S=9.3\\P=14.6\\y=2\ or \ y=7.3[/tex]
Replacing back in the Perimeter equation:
[tex]2x+2y=18.6[/tex]
if y=7.3
[tex]2x+2\cdot7.3=18.6\\2x+14.6=18.6\\2x=4\\x=2[/tex]
if y=2
[tex]2x+2\cdot2=18.6\\2x+4=18.6\\2x=14.6\\x=7.3[/tex]
So, the dimensions are 2 and 7.3 km
