The side lengths of a triangle are increased by 50% to make a similar triangle. does the area increase by 50% as well?

Yes it does.
For example if your side is 4 and your height is 3 your area would be 6
With the increased length your side would be 6 and height still 3 and your area would be 9

The are increased from 6 to 9 so it increased by 50%.

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)