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Distance between Two Points Using Pythagoras Theorem

In ΔABC, if A...

Question

In $Δ$ ABC, if AB = 7 cm and BC = 6 cm, which of the following is true?.

5 cm < AC < 11 cm

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1 cm < AC < 13 cm

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1 cm < AC < 10 cm

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2 cm < AC < 12 cm

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Solution

The correct option is B 1 cm < AC < 13 cm
Given: AB = 7 cm, BC = 6 cm

We know that sum of any two sides of a triangle is greater than third side.

In $Δ$ ABC,
AB + BC > AC
7 + 6 > AC
13 > AC ... (i)

BC + AC > AB
6 + AC > 7
AC > 1 ... (ii)
From equations (i) and (ii)
1 cm < AC < 13 cm

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