Respuesta :
Answer:
Option c - less than [tex]\sqrt{58}[/tex] inches but greater than 7 inches.
Step-by-step explanation:
Given : Ramon wants to make an acute triangle with three pieces of wood. So far, he has cut wood lengths of 7 inches and 3 inches.
To find : What length must the longest side be in order for the triangle to be acute?
Solution :
According to property of triangle,
If the square of larger side of triangle is equating to the sum of square of smaller side
If [tex]a^2<b^2+c^2[/tex] the triangle is acute triangle
where, a is the larger side and b,c are the smaller side
According to question, Let a=a , b=7, c=3
[tex]a^2<7^2+3^2[/tex]
[tex]a^2<49+9[/tex]
[tex]a<\sqrt{58}[/tex]
Means to be a acute triangle third side must be less than [tex]\sqrt{58}[/tex] inches but greater than 7 inches.
Therefore, Option c is correct.
