Question

What is the least value for an integer, x, for which x, x+5, and 2x−15 can be the lengths of the sides of a triangle?

Answer 1

11

Explanation:

Answer 2

• 11

Explanation:

Use triangle inequality

Each side length of the triangle is smaller than the sum of the other two side lengths

• x + x + 5 > 2x - 15 ⇒ 2x + 5 > 2x - 15, any value of x
• x + 2x - 15 > x + 5 ⇒ 2x > 2 + 15 ⇒ 2x > 20 ⇒ x > 10
• x + 5 + 2x - 15 > x ⇒ 2x - 10 > 0 ⇒ 2x > 10 ⇒ x > 5

The solution is x > 10 so the smallest integer value of x is 11.