A triangle is formed with edges along the line \(y=\frac{2}{3}x+5\), the \(x\)-axis, and the line \(x=k\). If the area of the triangle is less than \(20\), find the sum of all possible integral values of \(k\).

Guest Mar 8, 2020

#1**+2 **

The three vertices of the triangle are (-15/2, 0), (k, 0) and (k, 2k/3+5)

Hence base length b = k + 15/2 and height h = 2k/3 + 5

Calculate area from (1/2)bh and set equal to 20 to find the highest possible k. Take the floor value of the result as k is an integer. The lowest value of k is -7 since k must be greater than -15/2.

Hence determine the possible integer values of k and sum them.

Alan Mar 8, 2020