Question

Determine whether the given measures can be the lengths of the sides of a triangle. write yes or no. explain. 9.2, 14.5, 17.1

Answer 1

Answer with explanation:

If the length of three segments are, 9.2, 14.5 and 17.1 ,it can be sides of triangle if , Sum of two segments is greater than the third segment.

1.→ 9.2 +14.5=23.7 >17.1

2.→ 14.5 +17.1=41.6 > 9.2

3.→17.1 +9.2=26.3 >14.5

As, sum of any two segment is greater than third segment, so the following measurements can be the the lengths of the sides of a triangle.  

Answer 2

If the triangle has a angle of 90°, you can solved this exercise by applying the Pythagorean Theorem, which is:

 h²=a²+b²
 h=√(a²+b²)

 h: It is the hypotenuse (The opposite side of the right angle and the longest side of the triangle).

 a and b: They are the legs (The sides that form the right angle).

 The result of h=√(a²+b²), should be 17.1 (The longest side given in the problem). So, let's substitute the values of the legs into the Pythagorean equation:

 h=√(a²+b²)
 h=√((9.2)²+(14.5)²)
 h=17.1

 Therefore, the answer is:

 Yes, the given measures can be the lengths of the sides of a triangle.