Question

ABC is a triangle such that $AB=10\text{cm}$ and $AC=3\text{cm}$. Prove that the length of side BC is greater than 7 cm.

Answer 1

We know that sum of two sides of a triangle is always greater than the third side. (0.5 marks)

AC + BC should be greater than AB, which is 10 cm.
i.e., AC + BC > 10 (0.5 marks)
Given, AC = 3 cm
$\Rightarrow$ 3 + BC > 10 (0.5 marks)
$\Rightarrow$ BC > 10 - 3 (0.5 marks)
$\Rightarrow$ BC > 7 (0.5 marks)
$\Rightarrow$ BC should be greater than 7 cm. (0.5 marks)