## 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__

__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__

__To Find__

We need to determine

- Among the given choices, which range defines all possible values of x.

__Approach & Working__

__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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