In the figure below, the length of CB is 64 units and the length of BG is 137 units. What is the length of EA?
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To find the length of EA, we need to apply the triangle similarity property which states that if two triangles are similar, then their corresponding sides are proportional.
In this case, we can see that triangles CBA and EAG are similar.
To find the length of EA, we can set up the following proportion based on the corresponding sides:
CB/EA = BA/AG
Given that CB is 64 units and BG is 137 units, we can substitute the values into the proportion:
64/EA = BA/137
To find the length of BA, we need to first find the length of AB. To do this, we can subtract the length of CB from the length of BG:
AB = BG - CB = 137 - 64 = 73
Now we can substitute the values of BA and AB into the proportion:
64/EA = 73/137
To solve for EA, we cross-multiply and then divide:
64 * 137 = EA * 73
8788 = EA * 73
Finally, divide both sides by 73 to solve for EA:
EA = 8788/73 ≈ 120.33
Therefore, the length of EA is approximately 120.33 units.