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

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)   (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:

---------simple to solve.

.
.

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

Simplify and solve the system by substitution. Edwin

Answer by greenestamps(13200)   (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

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