Question 1203399
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Formal algebra is of course fine for solving the problem; and maybe a formal algebraic solution was wanted.<br>
But the problem looks to me like one for which an informal solution, using logical reasoning and simple arithmetic, is a useful exercise.<br>
When each leg was shortened by 7cm and the base was lengthened by 4cm, the change in the perimeter was 2(-7)+4 = -14+4 = -10.  So the perimeter of the new triangle is 46-10 = 36cm.<br>
The new triangle is equilateral, so each side length is 36/3 = 12cm.<br>
The base of the original triangle was lengthened by 4cm, so the base of the original triangle was 12-4 = 8cm.<br>
ANSWER: 8cm<br>