An isosceles triangle can be ‘sliced down the middle between the two equal sides to make two equal right angled triangles.
Let 6 be the base and 8 be the two equal sides pointing up. Here you would have two right angled triangles with a base 3 and a hypotenuse 8 so using Pythagoras you can work out the height is the square root of 64 minus 9 = 55^0.5.
Therefore the height is 55^0.5 and the area of the full triangle (not the half sized triangles which are right-angled)
= 0.5 times 6 times 55^0.5 = 3 times 55^0.5
From this you can work out the height if one of the equal sides (8cm) was the base instead of the different side (6cm).
Area = 3 times 55^0.5 = 0.5 times 8 times height = 4 times height
Therefore height when the base is 8 = 0.75 times 55^0.5
So the two possibilities are:
Base 6; height 55^0.5
Base 8; height 0.75 times 55^0.5
