A point R divides a line PQ internally in the ration 3:4. Another point S, divides the line PR externally in the ration 5:2. Given that PQ = 8cm, calculate the length of RS
R is 3/7 of the way along
S is 5/7 of the way along
RS is the difference: 2/7 * 8 = 16/7 cm
16/7
To calculate the length of RS, we need to find the lengths of PR and SR separately and then add them together.
First, let's find the length of PR. We know that R divides PQ internally in the ratio 3:4. This means that the length of PR is 3 parts out of 7 parts of PQ. Since PQ is 8 cm, we can calculate PR as follows:
PR = (3/7) * PQ
PR = (3/7) * 8 cm
PR = 3.43 cm (rounded to two decimal places)
Next, let's find the length of SR. We are given that S divides PR externally in the ratio 5:2. This means that the length of SR is 5 parts out of the sum of 5 parts and 2 parts of PR. We already know that PR is 3.43 cm, so we can calculate SR as follows:
SR = (5/7) * PR
SR = (5/7) * 3.43 cm
SR = 2.452 cm (rounded to three decimal places)
Finally, to find the length of RS, we need to add the lengths of PR and SR:
RS = PR + SR
RS = 3.43 cm + 2.452 cm
RS = 5.882 cm (rounded to three decimal places)
Therefore, the length of RS is approximately 5.882 cm.