The sides of a triangle have lengths of x, x + 4, and 20. If the longest side is 20, which of the following values of x would make the triangle acute?

A.
8
B.
10
C.
12
D.
14

Question

The sides of a triangle have lengths of x, x + 4, and 20. If the longest side is 20, which of the following values of x would make the triangle acute? 

A.
8
B.
10
C.
12
D.
14

campbell_st · Answer

you can use pythagoras' theorem in this question 

you need 

$$a^2 + b^2 > c^2$$

so substituting your sides you have 

$$x^2 + (x +4)^2 > 20^2$$

so use this to find the value of x

campbell_st · Answer

using the same rule for pythagoras, just check, which answer well give a value larger that 20^2

e.g. using the 1st choice  

is 

$$8^2 + 12^2 > 20^2~~~~or~~~~ 64 + 144 > 400$$