Geometry and TrigonometryVery hardSide of a triangle from a parallel segment
Geometry and Trigonometry practice question
In triangle PQR, point S lies on side PQ and point T lies on side PR so that segment ST is parallel to side QR. If PS = 4, SQ = 6, and ST = 6, what is the length of QR?
Answer: 15
Triangles PST and PQR are similar with ratio PS/PQ = 4/10, so QR = 6 × 10/4 = 15.
Common wrong answers
- If you answered 4
- 4 uses the ratio SQ/PS backwards.
- If you answered 9
- 9 uses the ratio SQ/PS = 6/4.
- If you answered 10
- 10 is PQ, not QR.
More Geometry and Trigonometry questions
- Very hard
Two parallel lines are cut by a transversal. One of the eight angles measures 47°. Which of the following is N… - Very hard
In a right triangle, angles A and B are the two acute angles, so A + B = 90°. If sin A = 0.6, what is the valu… - Very hard
A regular hexagon has a side length of 4. What is its area? (A regular hexagon of side s has area (3√3/2)s².) - Very hard
A cone has a radius of 6 and a height of 10. What is its volume? (Use V = (1/3)πr²h.) - Very hard
In the xy-plane, the graph of x² + y² − 12x − 4y + 15 = 0 is a circle. The line 3x − 4y = 25 intersects this c… - Very hard
What is the perimeter of triangle ABC?
Not affiliated with the College Board. SAT is a trademark of the College Board.