Question

The measure (in inches) of the sides of triangle RIO are equivalent to three consecutive odd integers. The perimeter is 201 inches. Which of the following statements are correct? Select all that apply. The triangle is obtuse. The triangle is scalene. The smallest side measures 61 inches. The largest side measures 69 inches. If triangle RIO is dilated of 1/3, then the perimeter of the dilated triangle will be 3 units smaller.

Answer 1

Let 
x-------------> first odd integer
x+2---------> second odd integer
x+4---------> third odd integer

we know that
(x)+(x+2)+(x+4)=201--------> 3x+6=201--------> 3x=195-------> x=65

the three sides of triangle RIO are 
x=65 in
x+2-----> 65+2-----> 67 in
x+4----> 65+4------> 69 in

then
69²=4761----------> c²
(65²+67²)=8714--------> a²+b²
c² < (a²+b²)---------> the triangle RIO is not obtuse
Is acute angle triangle

statements 
1) The triangle is obtuse--------> is false
Is acute angle triangle

2) The triangle is scalene-----> is correct
The three sides measures are diferent 

3)The smallest side measures 61 inches--------> is false
The smallest side measures 65 in

4)The largest side measures 69 inches-------> is correct

5) If triangle RIO is dilated of 1/3, then the perimeter of the dilated triangle will be 3 units smaller
If triangle RIO is dilated of 1/3, then news sides are
65/3------> 21.67 in
67/3-------> 22.33 in
69/3------> 23 in

the new perimeter is=21.67+22.33+23------> 67 in
201-67=134 in
therefore
If triangle RIO is dilated of 1/3, then the perimeter of the dilated triangle will be 3 units smaller----------> is false

Because the perimeter of the dilated triangle will be 134 units smaller

Answer 2

Answer: the triangle is scalene

The largest side measures 69 inches

Step-by-step explanation: