To find the value of [tex]\( l(BD) + l(CG) - l(FP) \)[/tex], we will use the given lengths:
- Length of [tex]\( BD \)[/tex] is [tex]\( \frac{9}{8} \)[/tex] units.
- Length of [tex]\( CG \)[/tex] is [tex]\( \frac{3}{8} \)[/tex] units.
- Length of [tex]\( FP \)[/tex] is [tex]\( \frac{3}{6} \)[/tex] units.
First, simplify the length of [tex]\( FP \)[/tex]:
[tex]\[
\frac{3}{6} = \frac{1}{2}
\][/tex]
Next, we calculate the sum of the lengths of [tex]\( BD \)[/tex] and [tex]\( CG \)[/tex]:
[tex]\[
l(BD) + l(CG) = \frac{9}{8} + \frac{3}{8}
\][/tex]
Since the denominators are the same, simply add the numerators:
[tex]\[
\frac{9}{8} + \frac{3}{8} = \frac{12}{8} = \frac{3}{2}
\][/tex]
Now, subtract the length of [tex]\( FP \)[/tex]:
[tex]\[
\frac{3}{2} - \frac{1}{2}
\][/tex]
Again, since the denominators are the same, subtract the numerators:
[tex]\[
\frac{3}{2} - \frac{1}{2} = \frac{2}{2} = 1
\][/tex]
Thus, the value of [tex]\( l(BD) + l(CG) - l(FP) \)[/tex] is [tex]\( 1.0 \)[/tex] units.
So the correct answer is:
[tex]\[
\boxed{1}
\][/tex]
