Question

The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequality can be used to find the possible lengths, x, of the base of the triangle?

Answer 1

Let x be the base of the triangle, and
      2x + 4 be the height. 

One of the ways in solving for the area of a triangle is to half the product of its height (h) and base (b). Mathematically,
 
                              A = bh / 2

Substituting the expression for b and h and the given condition for the area,
   
                                    (x)(2x + 4) / 2 ≤ 168