Question

A triangle's area is given by the expression 3x2 – x + 12. The height is 6x. The base of the triangle is the quotient of the area and of the height.



Which expression represents the base of the triangle?


x – + 4x
+ 4x
x –

Answer 1

Area = 1/2 · base · height, so base = (2 · area)/height.

base = [2(3x^2 − x + 12)]/(6x) = (6x^2 − 2x + 24)/(6x) = (3x^2 − x + 12)/(3x)
= x − 1/3 + 4/x (for x ≠ 0).

So the base is x − 1/3 + 4/x.