To determine the value of [tex]\( a \)[/tex] given that [tex]\( c = 10 \)[/tex], we should evaluate each option provided:
1. The first option is [tex]\( a = 1 \)[/tex]. This is a numerical value without any relation to [tex]\( c \)[/tex].
2. The second option is [tex]\( a = 5 \)[/tex]. This is another numerical value without any direct relation to [tex]\( c \)[/tex].
3. The third option is [tex]\( a = 20 \)[/tex]. This also is a numerical value without direct relation to [tex]\( c \)[/tex].
4. The fourth option is [tex]\( a = 5 \sqrt{3} \)[/tex]. Here, [tex]\( a \)[/tex] is expressed as a multiple of the square root of 3, but we need to check how it relates to [tex]\( c = 10 \)[/tex].
5. The fifth option is [tex]\( a = 10 \sqrt{3} \)[/tex]. This suggests that [tex]\( a \)[/tex] is 10 times the square root of 3.
We need to check which of these values correctly fits the condition when [tex]\( c = 10 \)[/tex].
Let's calculate:
- For [tex]\( a = 10 \sqrt{3} \)[/tex]:
[tex]\[
10 \sqrt{3} \approx 10 \times 1.732050807568877
\][/tex]
[tex]\[
= 17.32050807568877
\][/tex]
Among the options, this value fits distinctly with [tex]\( c = 10 \)[/tex], and therefore, it meets the required criteria.
Thus, the value of [tex]\( a \)[/tex] when [tex]\( c = 10 \)[/tex] is [tex]\( 10 \sqrt{3} \)[/tex].
So, the correct value of [tex]\( a \)[/tex] is [tex]\( 10 \sqrt{3} \)[/tex].
