Question

What are the lengths of the three sides of a triangle with a perimeter of 3071 miles, knowing that the shortest side measures 78 miles less than the middle side, and the longest side measures 371 miles more than the middle side?

A) 797 mi, 1246 mi, 1028 mi
B) 897 mi, 1346 mi, 1028 mi
C) 947 mi, 1376 mi, 1078 mi
D) 897 mi, 1376 mi, 1078 mi

Answer 1

After setting up an equation where x represents the middle side, calculating based on the relationships between sides and the perimeter, we find that the sides of the triangle measure 848 miles, 926 miles, and 1297 miles. These do not match any of the given options.

Step-by-step explanation:

To find the lengths of the three sides of the triangle, we set up equations based on the given perimeter and the relationships between the sides:

• Let x represent the length of the middle side.
• The shortest side is then (x - 78) miles.
• The longest side is (x + 371) miles.
• The perimeter is the sum of all three sides, which is given as 3071 miles.

The equation for the perimeter is:

x + (x - 78) + (x + 371) = 3071

Solving for x, we combine like terms:

3x + 293 = 3071

Subtract 293 from both sides:

3x = 2778

Divide both sides by 3:

x = 926

Now, find the lengths of the other two sides:

• Shortest side: 926 - 78 = 848 miles
• Longest side: 926 + 371 = 1297 miles

The lengths of the three sides are 848 miles, 926 miles, and 1297 miles. These lengths correspond to none of the given options (A, B, C, D), implying there may be an error in the question or the provided options.