Question 16932
The lengths of the sides of a triangle are 3t,5t-12, and t+20 
Find the value(s) of t that make the triangle isosceles
in an isocelles triangle 2 sides will be equal.also we should check ,primafacie ,whether a triangle can be drawn by verifying that sum of any 2 sides is greater than the third side.
case 1 ...3t=5t-12 or 5t-3t=12 or t=6...in  this case 2 sides are 18 each and the third side is 6+20=26...18+18=36>26..so ok.
case 2....3t=t+20 or 2t=20 or t=10....in this case 2 sides are 30 each and the third side is 5*10-12=50-12=38....30+30>38...so ok.
case 3.....5t-12=t+20 or 5t-t=20+12=32 or t=8...in this case 2 sides are 28 each and the third side is 3*8=24....32+32=64>24....so ok.