Two sides of an acute triangle measure 5 inches and 8 inches. the length of the longest side is unknown.
what is the greatest possible whole-number length of the unknown side?
8 inches
9 inches
12 inches
13 inches

Answer. 9 inches

1. Using some logical reasoning(Not proving because it will take a while) as the acute angle approaches to 90° the side in front of that angle extends.

2. Lets find the third side if the angle is 90° -> Using Pythagoras's theorem` hypotenuse(the side)=√(5*5+8*8) which is approximately 9.433 inches.

3. As we need to find the largest possible length of the unknown side its 9 inches, which is the biggest integer below 9.4.

Option 2 - 9 inches    

Step-by-step explanation:

Given : Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown.

To find : What is the greatest possible whole-number length of the unknown side?

Solution :

Applying Pythagorean Theorem,

If c is the longest side of a acute triangle, a and b are other two sides of a acute triangle then the condition is given as,

We have given, P=5 , B=8

Substitute,

To the greatest possible whole number length of unknown side is 9 inches.

Therefore, Option 2 is correct.

24 units

step-by-step explanation: