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# A triangle is formed with edges along the line , the -axis, and the line . If the area of the triangle is less than

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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 $$k$$.

Mar 8, 2020

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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.

Mar 8, 2020