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jmc

algebra senior

Problem

A two-row triangle is created with a total of 15 pieces: nine unit rods and six connectors, as shown. What is the total number of pieces that would be used to create an eight-row triangle?

problem
Solution
We'll start with rods. The first row has 3 rods, the second row has 6 rods, and continuing down, we see that the next rows have 9, 12, 15, and so on rods. So the total number of rods in an eight-row triangle is For the connectors, note that in an -row triangle, the connectors form a triangle which has rows. For example, a two-row triangle has three rows of connectors, and connectors. So an eight-row triangle has connectors. We have a total of pieces.
Final answer
153