Question

What is the value of x, such that the perimeter of a triangle with side lengths 14, x + 4, and 2x - 3 is at least 57?

a) x = 15
b) x = 17
c) x = 18
d) x = 19

Answer 1

The value of x that satisfies the inequality for the perimeter of the triangle to be at least 57 is x = 15.

Step-by-step explanation:

The question asks us to find the value of x such that the perimeter of a triangle with side lengths 14, x + 4, and 2x - 3 is at least 57. To solve this, we set up an inequality:

14 + (x + 4) + (2x - 3) ≥ 57

Combining like terms, we get:

14 + x + 4 + 2x - 3 ≥ 57

3x + 15 ≥ 57

Subtracting 15 from both sides of the inequality:

3x ≥ 42

Dividing both sides by 3 gives:

x ≥ 14

From the options provided, the smallest value of x that satisfies this inequality is x = 15 (option a). Therefore, the correct answer is x = 15 which ensures the perimeter of the triangle is at least 57.