Final answer:
To find the original base length of the isosceles triangle, we set up equations based on the given perimeter and the condition for the triangle turning into an equilateral triangle after changes to its sides. Solving these equations, we find that the original base length is 19 cm.
Step-by-step explanation:
The student is asking about solving a problem related to the perimeter of an isosceles triangle and finding the original base length given certain conditions that would turn it into an equilateral triangle.
In the original isosceles triangle, we'll denote the equal sides as 'a' and the base as 'b'. Since the perimeter is the sum of all sides, we have:
a + a + b = 75 cm
When altered, the base becomes 'b + 2 cm' and the equal sides become 'a - 7 cm'. To form an equilateral triangle, all sides must be equal:
b + 2 = a - 7
Simplifying gives us two equations:
Rearranging the second equation we get a = b + 9. Substituting 'a' in the first equation we get:
2(b + 9) + b = 75
Which simplifies to:
3b + 18 = 75
b = 19 cm
Therefore, the length of the base of the original isosceles triangle is 19 cm.