OGQR 2020: Question No. 91
Which of the following gives all possible values of x in the figure above?
| Source | OGQR 2020 |
| Type | Problem Solving |
| Topic | Geometry |
| Sub-Topic | Triangle |
| Difficulty | Easy – Medium |
Solution
Given
In this question, we are given
- The diagram of a triangle PQR, with side lengths PQ = 3, QR = 4, and PR = x
To Find
We need to determine
- Among the given choices, which range defines all possible values of x.
Approach & Working
We know that, for any given triangle, sum of any two sides is always greater than the third side.
Therefore, we can say
- 3 + 4 > x
Or, x < 7
Similarly, x + 4 > 3
Or, x > 1
Combining the two results, we can conclude 1 < x < 7.
Hence, the correct answer is option B.
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