Question

If two sides of the triangle are given as 8 feet and 11 feet, the inequality representing the range of length of third side 'y' (in feet) is

• A. y < 3
• B. 8 < y < 11
• C. 3 < y < 19
• D. y > 19

Answer 1

The correct option is C 3 < y < 19

Let the length of the third side be 'y' feet.

According to the triangle inequality theorem, the sum of two sides of a triangle is greater than the length of the third side and the difference between the two sides is always smaller than the third side.

So, the inequality can be expressed as:
$11-8<y<11+8$
$\Rightarrow 3<y<19$

∴ The length of the third side (y) will be between 3 and 19 feet.