To determine the correct side lengths [tex]$a$[/tex] and [tex]$b$[/tex] to two decimal places, we will compare each of the given choices to find the one that matches the expected values.
Given that we know the actual side lengths to be:
[tex]\[ a = 11.0 \][/tex]
[tex]\[ b = 15.0 \][/tex]
Let's examine the provided options:
A. [tex]\( a = 11.40 \)[/tex] and [tex]\( b = 13.38 \)[/tex]
- This does not match as [tex]\( a = 11.40 \)[/tex] and [tex]\( b = 13.38 \)[/tex] are not equal to 11.0 and 15.0.
B. [tex]\( a = 10.92 \)[/tex] and [tex]\( b = 14.52 \)[/tex]
- This does not match as [tex]\( a = 10.92 \)[/tex] and [tex]\( b = 14.52 \)[/tex] are not equal to 11.0 and 15.0.
C. [tex]\( a = 4.18 \)[/tex] and [tex]\( b = 3.15 \)[/tex]
- This does not match as [tex]\( a = 4.18 \)[/tex] and [tex]\( b = 3.15 \)[/tex] are not equal to 11.0 and 15.0.
D. [tex]\( a = 11 \)[/tex] and [tex]\( b = 15 \)[/tex]
- This matches perfectly as [tex]\( a = 11.0 \)[/tex] and [tex]\( b = 15.0 \)[/tex].
Thus, the correct choice that matches the given side lengths is:
D. [tex]\( a = 11.0 \)[/tex] and [tex]\( b = 15.0 \)[/tex]
