The perimeter of a triangle with two equal sides is 50 cm. If its base were lengthened by 3 cm and each leg were shortened by 4 cm, all three sides would be equal. Find the length of the base of the original triangle.

Base of the original triangle is 12 cm.

Step-by-step explanation:

Let base of triangle be x

two equal legs of triangles by y

therefore perimeter of triangle

x+y+y = 50 or x+2y = 50

according to the question

if base is x+3 and leg is y-4

then both are equal

that is x+3 = y-4

y-x = 7 or y = x+7

x+2y = 50

x+2 (x+7) = 50

x+2x + 14 = 50

3x + 14 = 50

3x = 50 - 14

3x = 36

x = 12

therefore base of the original triangle is 12 cm