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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
 #1
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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

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