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Georgia [21]
2 years ago
10

a certain triangle has a perimeter of 3067 mi. the shortest side measures 71 mi less than the middle side and the longest side m

easures 372 mi more the the middle. the shortest side is how many mi long
Mathematics
1 answer:
UkoKoshka [18]2 years ago
6 0

Answer:

The measure of the shortest side is 851 miles

Step-by-step 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

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<em>Additional comment</em>

There are several ways this can be explained. One of them makes use of the relation between rectangular and polar coordinates:

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Answer:

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Step-by-step explanation:

Solve the following system:

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