Find the exact length of the third side.
48
55

This sounds like a traditional question regarding the Pythagorean Theorem. 

In any right triangle, the sum of the squares of the legs of the sides will always be equal to the squared length of the hypotenuse. 

This is expressed as a^2 +b^2 = c^2

To solves, plug in your numbers. The two lengths that you are provided with are 48 inches and 55 inches. 

Assuming these two values represent the lengths of the legs of the triangle we can therefore write the following: 

48^2 + 55^2 = c^2 

Simplifying we arrive at the following: 

2304 + 3025 = c^2

5239 = c^2

To solve for c^2 you take the square root of 5239 and arrive at 73.

However, you were asked in your problem what the longest possible measurement of the third side of the triangle is, meaning we have speculated that the two values given you were the legs of the triangle, and NOT the hypotenuse, you see? 

So, now you must do the exact same thing with the problem, allowing the value of 48 be the length of the hypotenuse in one case, and in the next allow 55 to be the value of the hypotenuse. Why? Because doing so allows you to KNOW with certainty what the longest possible measurement of the third side could be. 

So, instead of making you go through all of this on your own, I am going to work the problem two more times. Remember, we have already found a value of 73 for one length. 

Now, let's assume 48 is the hypotenuse, okay? 

Going back to our original Pythagorean Theorem we KNOW a^2 + b^2 =c^2

So, it matters little which SIDE we assign one of the values given because of the theorem. 

Let's go with a = 48 and the hypotenuse being 55 okay? 

48^2 + b^2 = 55^2 

Now, solve for b. 

2304 + b^2 = 3025

b^2 = 721

b = 26.85 or rounding up 26.9 

Now, let's do the other possibility, shall we? 

Let the hypotenuse be 48 and one of the other legs be 55. 

a^2 + b^2 = c^2

3025 + b^2 = 48^2 Solve for b

3025 = b^2 = 2304

And immediately you KNOW with utter certainty that there is no way this value works. Why? Because if you solve for b you would need to subtract the 3025 from 2304, leaving you with a negative value, meaning the triangle would not be. 

Therefore, you KNOW the longest possible measurment of the third side of that triangle, due to the Pythagorean Theorem is 73 inches. 

Step-by-step explanation:

Plz like it

its a little blurry tbh

step-by-step explanation: