Question

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

Answer 1

see for a triangle, the sum of any two sides must be greater than the third side.. so
x+(x+4)>20 gives 2x>16 gives x>8

Answer 2

now we have to find the condition for which the triangle will be acute

Answer 3

for the triangle to be acute a^2+b^2>c^2 where a,b, c are the length of the sides and c is the longest side

Answer 4

here a=x,b=x+4 and c=20
so you need to solve for x when x^2+(x+4)^2>20^2

Answer 5

this gives on simplification (x+16)(x-12)>0

Answer 6

hence x>12

Answer 7

again x+4<20 this gives x<16 so we have an inequality 12<x<16

Answer 8

@jmitch98