SOLUTION: The perimeter of a triangle is 46 cm. The triangle is isosceles now, but if its base were lengthened by 4 cm and each leg were shortened by 7 cm, it would be equilateral. Find the

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Question 1203399: The perimeter of a triangle is 46 cm. The triangle is isosceles now, but if its base were lengthened by 4 cm and each leg were shortened by 7 cm, it would be equilateral. Find the length of the base of the original triangle.
Found 3 solutions by josgarithmetic, Edwin McCravy, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You can draw the figure.
If k for each leg and b for base length of original isosceles triangle then:

system%282k%2Bb=46%2Cand%2Cb%2B4=k-7%29---------simple to solve.

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system%28k=19%2Chighlight%28b=8%29%29

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


system%28y%2By%2Bx=46%2Cy-7=x%2B4%29

Simplify and solve the system by substitution.

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Formal algebra is of course fine for solving the problem; and maybe a formal algebraic solution was wanted.

But the problem looks to me like one for which an informal solution, using logical reasoning and simple arithmetic, is a useful exercise.

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.

The new triangle is equilateral, so each side length is 36/3 = 12cm.

The base of the original triangle was lengthened by 4cm, so the base of the original triangle was 12-4 = 8cm.

ANSWER: 8cm