Please help. I'm completely stuck.

Question

The perimeter of a triangle is 75cm. The triangle is isosceles now, but if its base was lengthened by 2cm and each leg were shortened by 7cm, it would be equilateral. Find the length of the base of the original triangle.

Answer 1

Let the legs each be x cm, and let the base be y cm.

Thus, we have:

2x + y = 75 --- (1)
x - 7 = y + 2 --- (2)

From (2), we have:

x - 7 = y + 2
y = x - 9 --- (3)

Substituting (3) into (1), we will get:

2x + x - 9 = 75
3x - 9 = 75
3x = 84
x = 28

Substituting 28 into (3), we will get:

y = 28 - 9
y = 19

Hence, the original base of the triangle is 19 cm