Let h represent the height of the triangle.
... b = 10 + 3h . . . . . . the base is 10 inches more than 3 times the height
... A = (1/2)bh . . . . . . formula for the area of a triangle in terms of base and height
... 16 = (1/2)(10 +3h)h . . . . substitute the known values
... 3h² + 10h - 32 = 0 . . . . rearrange to standard form
... (h -2)(3h +16) = 0
... h = 2 or -16/3 . . . . . . . . the negative solution is extraneous
... b = 10 + 3·2 = 16 . . . . . use the relation between b and h
The base and height of the triangle are 2 inches and 16 inches, respectively.
