Calculate the length of line segment P R ‾ \overline{PR} given the diagram below & P Q = 24 PQ= 24 inches & Q R = 3 8 P Q QR=\frac38PQ .

Welcome back. In this problem, we'd like to calculate the length of segment PR given the diagram below, and PQ equals 24 and QR equals 3/8 PQ. Now, we want to find the length of segment PR and below we have pictured line PR. Segment PR is just this distance here that extends from point P to point R. So we want to find this entire length. Now, we can see that this line segment is broken up into two pieces. We have our first piece, which is PQ, and we have our second piece, which is QR. Now, we know that PQ has a length of 24. If we can find the length of QR, we can just add the length of PQ and the length of QR to get the length of PR, and that's what we're gonna do here. Now, we don't currently know the length of QR, but we are told that QR is equal to 3/8 PQ. So we have QR is equal to 3/8. PQ. Well, we do know that PQ is 24, so we can rewrite this as QR is equal to 3/8 times 24. Again, by just plugging in the length of PQ which is 24. Now, we need to multiply 3/8 and 24. You could do this by hand or on your calculator, but 1/8 of 24 is 3, so 3/8 is going to be 9, and we end up getting that QR is equal to 9. So we know that this piece here is 9. As we said before, PR is going to be equal to the length of PQ. Plus the length of QR. And now we know what each of those pieces is. We know that PQ is 24, and we know that QR is 9. 24 plus 9 is 33, so PR has a length of 33, and specifically, we can see the unit is inches here, so we can say that PR is 33 inches. Great work.