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Which of the following gives all possible values of x in the figure above? – OGQR 2020 Question #91 with Solution

OGQR 2020: Question No. 91

Which of the following gives all possible values of x in the figure above?

SourceOGQR 2020
TypeProblem Solving
TopicGeometry
Sub-TopicTriangle
DifficultyEasy – 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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