Question

$\text{ABC is a triangle such that AB = 10 cm}\text{and AC = 3 cm. Which of the following}\text{statements are true?}$

• A. $BC>7cm$
• B. $BC=6cm$
• C. $BC<13cm$
• D. $BC=14cm$

Answer 1

Answer: (A), (C)

The correct options are
A

$BC>7cm$

C

$BC<13cm$

We know that sum of two sides of a traingle is always greater than its third side.

$\Rightarrow AC+AB>BC$

$\Rightarrow (3+10)cm>BC$

$\Rightarrow BC<13cm$

Also, the difference between its two sides is less than the third side

$\Rightarrow AB-AC<BC$

$\Rightarrow (10-3)cm<BC$

$\Rightarrow 7cm<BC$

$\Rightarrow BC>7cm$

$\text{Thus, 7 cm < BC < 13 cm}.$