If we call the base x, then we can call the height (x - 4). The area of a triangle is (base × height)/2, so we can put that into an equation:
(x × (x - 4))/2 = 48
(x² - 4x)/2 = 48
× 2
x² - 4x = 96
- 96
x² - 4x - 96 = 0
(factorise)
(x - 12)(x + 8)
x = 12 or x = -8, and you can't have negative lengths, so the answer is 12m.
I hope this helps! I did a few things without explaining them so let me know if you would like me to go over in more detail :)
