OGQR 2020: Question No. 97
The figure above represents an antenna tower with two guy wires that extend from point Q, 40 feet above the ground, to points P and R as shown. If the two wires have equal length, approximately what is the total length, in feet, of the two wires?
| Source | OGQR 2020 |
| Type | Problem Solving |
| Topic | Geometry |
| Sub-Topic | Triangles |
| Difficulty | Medium |
Solution
Given
In this question, we are given
- The given figure represents an antenna tower with two guy wires that extend from point Q, 40 feet above the ground, to points P and R as shown.
- The two wires have equal length.
To Find
We need to determine
- The total approximate length, in feet, of the two wires.
Approach & Working
As the lengths of two wires are same, PQ = QR.
Hence, PQR is an isosceles triangle.
- In an isosceles triangle, perpendicular from the top vertex to the base bisects the base.
- Therefore, each of the two right-angled triangles has a base of 30 feet.
Hence, we can say
- QR2 = 302 + 402 = 502
Or, QR = 50
Thus, the length of the two wires combined = (50 + 50) feet = 100 feet
Hence, the correct answer is option C.
Begin your GMAT preparation with the only prep company that has delivered more 700+ scores than any other GMAT club partner. Achieve GMAT 740+ with our AI driven tools that you personalized feedback at every step of your GMAT journey. Take our free trial today!
