She used 54 inches. 3/4 is equal to .75 so you can find 3/4 of the board by taking the fool length and multiplying it by .75 so 6•.75=4.5. So 3/4 of the board is 4.5 ft. However, the answer has to be in inches so since there are 12 inches in a foot you multiply 4.5•12 and that gives you your answer:54 inches.
So anytime we have a slope and want to find the slope of a perpendicular line, we just have to remember a perpendicular line's slope is the negative reciprocal (reciprocal means flip the fraction). So if we had a slope of 3/4, the slope perpendicular to it would be - 4/3.
First we need to find our slope, to do this we take the change in y over the change in x like so:
