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Work Shown:
Because segment GI is parallel to segment TA, this means triangle VGI is similar to triangle VTA.
From that we can set up the proportion
VG/VT = VI/VA
which breaks down into
VG/(VG+GT) = VI/(VI+IA)
Let's plug in the given values. Let x be the length of segment IA.
Let's solve for x
VG/(VG+GT) = VI/(VI+IA)
72/(72+61) = 95/(95+x)
72/133 = 95/(95+x)
72(95+x) = 133*95 ......... cross multiply
6840+72x = 12635
72x = 12635-6840
72x = 5795
x = 5795/72
x = 80.4861111111111 ......... which is approximate
x = 80.49 ......... rounding to the nearest hundredth
The length of IA is roughly 80.49 units. This is not the final answer. The fact that 80.49 is listed as one of the answer choices seems to imply your teacher put it as a trick answer.
Since we found IA = 80.49, this means,
VA = VI + IA
VA = 95 + 80.49
VA = 175.49
This is the length of segment VA, which is the same as segment AV.
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Here's a slightly similar way to solve:
VT = VG+GT = 72+61 = 133
VG/VT = VI/VA
72/133 = 95/x
72x = 133*95
72x = 12635
x = 12635/72
x = 175.486111111111
x = 175.49 is the approximate length of segment AV.
