SOLUTION: A triangle has a perimeter of 3075 miles. The shortest sides measures 75 miles less than the middle, and the longest side measures 375 miles more than the middle side. Algebraicall

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Question 212455: A triangle has a perimeter of 3075 miles. The shortest sides measures 75 miles less than the middle, and the longest side measures 375 miles more than the middle side. Algebraically, find the length of the three sides.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A triangle has a perimeter of 3075 miles. The shortest sides measures 75 miles less than the middle, and the longest side measures 375 miles more than the middle side. Algebraically, find the length of the three sides.

Step 1. Let P = Perimeter = 3075 miles. A triangular perimeter means adding the three sides.

Step 2. Let x = middle side

Step 3. Let x-75 = shortest side

Step 4. Let x+375 = longest side

Step 5. Use Steps 1-4 to get

P+=+x%2Bx-75%2Bx%2B375

P+=+3x-75%2B375

P+=+3x%2B300

P+=+3075+=+3x%2B300

Step 6. Solve for x. Subtract 300 from both sides of equation to isolate 3x term.

3075-300+=+3x%2B300-300

2775+=+3x

Divide by 3 to get x

2775%2F3+=+3x%2F3

925+=+x

x-75+=+925+-+75+=++850

x%2B375=+925+%2B+375+=+1300+

Step 7. Check Perimeter P with above values
P=925%2B850%2B1300=3075 Answer ok.

Step 7. Answer is that the sides of the triangle are 925, 850 and 1300.

I hope the steps were helpful and clear. Good luck in your studies.


Respectfully,
Dr J

For Step-By-Step videso on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.