In a triangle, we have line QR parallel to line ST, PQ = 8, QS = 6, and PT = 12. Find PR.
YES
6.86
To find PR in the given triangle, we can use the property of parallel lines and proportionality of sides.
Here's how we can solve it step by step:
Step 1: Draw the triangle and the parallel lines.
- Draw a triangle with vertices P, Q, and T.
- Draw a line QR parallel to line ST.
Step 2: Identify the given information.
- PQ = 8
- QS = 6
- PT = 12
Step 3: Use the property of parallel lines and proportionality of sides.
- Since QR is parallel to ST, we can use the property of parallel lines to form similar triangles.
- From the similarity of triangles, we can set up the following proportion:
PQ/PT = QS/QR
Step 4: Substitute the given values.
- Substitute the known values into the proportion:
8/12 = 6/PR
Step 5: Solve the proportion for PR.
- Cross-multiply and solve for PR:
8PR = 6 * 12
8PR = 72
PR = 72/8
PR = 9
Step 6: Determine the answer.
- Therefore, PR = 9 units.
So, in the given triangle, line PR measures 9 units.