In ΔABC, BC = 10 cm, CA = 15 cm then the measure of AB is
In ΔABC, BC = 10 cm, CA = 15 cm then the measure of AB is
A) Less than 25 cm
B) Greater than 25 cm
C) Equal to 25 cm
D) Less than 5 cm
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2 Answers
Correct option is (A) Less than 25 cm
\(\because\) Sum of any two sides is always greater than the third side in a triangle.
\(\therefore\) In \(\triangle ABC\), BC+CA > AB
\(\Rightarrow\) AB < 10+15
\(\Rightarrow\) AB < 25 ________(1)
Also difference of any two side is always less than the third side in a triangle.
\(\therefore\) CA - BC < AB
\(\Rightarrow\) 15 - 10 < AB
\(\Rightarrow\) AB > 5 ________(2)
\(\therefore\) From (1) and (2), 5 < AB < 25
Hence, option (A) is correct.
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