Question

a certain triangle has a perimeter of 3064 mi. the shortest side measures 78 mi less than the middle side, and the longest side measures 373 mi more than the middle side. find the lengths of the three sides. the shortest side is 845 mi long. the middle side is □ mi long.

Explanation:

Step1: Define the middle side

Let the length of the middle side be \( x \) miles. Then the shortest side is \( x - 78 \) miles (since it's 78 mi less than the middle side), and the longest side is \( x + 373 \) miles (since it's 373 mi more than the middle side). We know the shortest side is 845 mi, so we can set up the equation for the shortest side: \( x - 78 = 845 \).

Step2: Solve for the middle side

To find \( x \), we add 78 to both sides of the equation \( x - 78 = 845 \). So, \( x = 845 + 78 \). Calculating that, \( 845 + 78 = 923 \).

Answer:

923