1. We are given:
[tex]a^2 = 64[/tex]
The only a which squared gives you 64 is 8. The perimeter of an 8 by 8 square will be 32. Half of that is 16. Now, let's see what we can do. We can set up:
[tex]4a = 16[/tex]
Obviously, each side length has to be 4. So, the area of this square will be 16 units².
2. Let n equal her son's age. So, her age right now will be (S = her age):
[tex]S = 18n[/tex]
1 year ago it was:
[tex]S-1 = 3n[/tex]
We have 2 equations, let's substitute. We can rewrite this as:
[tex]18n-1 = 3n[/tex]
Solve for n:
[tex]15n-1=0[/tex]
[tex]n= \frac{1}{15} [/tex]
We know the value of n, which is her son's age. So, her son is 1/15 of a year old or about 24 days old.
