One side of an isosceles triangle has a length of 19 m. the lengths of the other two sides are equal to one another, but are unknown. if the perimeter of the triangle is 51 m, what is the length of each unknown side?

Let x= side 1= 19
Let y= side 2=unknown
Let z= side 3=unknown
Since it is an isosceles triangle, two sides are equal, which happen to be y and z
Hence y=z

Perimeter of a triangle = Sum of all three sides
= x+y+z
51=19+2y [since we know x=19 and y=z, we know the perimeter is 51]
Solve now
32=2y
16=y
Since y=z
z= 16
Hence the unknown side's length is 16m

So the perimeter is 51. The base is 19. Subtract 19 from 51. 51 - 19 = 32. So 32 is the total length of the two equal unknown sides added together. Because the two sides must be equal, you can just divide 32 by 2. 32/2 = 16. Each of the two congruent sides are 16 m.