The height of a triangle is 4 m less than its base. The area of the triangle is 48 m².

What is the length of the base?

Let the height be h and base = b

then h=b-4

area = 1/2 x b x h

48 = 1/2 x b x (b-4)

48 = 1/2 x b^2 - 4b

2 x 48 = b^2 - 4b

b^2 - 4b - 96=0

b2 - 12b + 8b - 96 = 0

b (b-12) + 8 (b-12) = 0

either b = 12 m or b=-8 (rejected)

hence, base = 12m and height = 8 m