Question

a certain triangle has a perimeter of 3067 mi. the shortest side measures 71 mi less than the middle side and the longest side measures 372 mi more the the middle. the shortest side is how many mi long

Answer 1

The measure of the shortest side is 851 miles

Explanation:

Let

x ----> the measure of the shortest side

y ---> the measure of the middle side

z ---> the measure of the longest side

we know that

The perimeter of triangle is equal to

`P=x+y+z`

`P=3,067\ mi`

so

`3,067=x+y+z` ----> equation A

the shortest side measures 71 mi less than the middle side

so

`x=y-71` ----> equation B

the longest side measures 372 mi more the the middle side

so

`z=y+372` ----> equation C

substitute equation B and equation C in equation A

`3,067=(y-71)+y+(y+372)`

solve for y

`3,067=3y+301\\3y=2,766\\y=922`

Find the value of x

`x=y-71\\x=922-71\\x=851`

therefore

The measure of the shortest side is 851 miles