The side of a triangle have length x, x+4, and 20. If the length of the longest side is 20, which value of x would make the triangle acute?

12∠x∠16

Step-by-step explanation:

For the triangle to be acute, a²+b²+c²,

Where c is the largest side of the triangle.

Hence, we must say x² + (x+4) ²≥20²,

or after simplifying, x²+4x-192≥0 or (x+16) (x-12) ≥0

Since x must have positive values only, x≥12

Therefore, for the triangle to be acute, we must have 12≤x≤16.