Answer :
Answer:
(1) Insufficient data
(2) Sufficient data
Step-by-step explanation:
We need to check whether the given data is sufficient or not to prove that a rectangular region has perimeter P inches and area A square inches, is the region square.
Assume that the given conditions are
1. [tex]P=\frac{4}{3}A[/tex]
2. [tex]P=4\sqrt{A}[/tex]
Area of square is
[tex]A=a^2[/tex]
Taking square root on both sides.
[tex]\sqrt{A}=a[/tex] .... (1)
where a is side length.
Perimeter of square is
[tex]P=4a[/tex] ... (2)
From (1) and (2) we get
[tex]P=4\sqrt{A}[/tex]
It means second condition is sufficient to prove that the rectangle reason is square, because it is true for all.
For a=3,
A=9 and P=12
[tex]12=\frac{4}{3}(9)[/tex]
[tex]12=12[/tex]
LHS=RHS
For a=6,
A=36 and P=24
[tex]24=48[/tex] (False statement)
The first condition is insufficient because it may or may not be true.