The perimeter of a triangle is 30 feet. The longest side is 1 foot longer than the medium side, and the shortest side is 7 feet shorter than the medium side. What is the length of the longest side?

Answer 1

Three sides are m, m + 1, and m - 7

The sum of these three is 30.

Can you solve for m and answer?

Is this really a precalculus queston?

Answer 2

We can set this problem up by assigning names to the different side lengths. Choose L, M, and S to be the longest, medium, and shortest sides, respectively. Now we can write some equations involving these variables from the given information:

1. "The perimeter of a triangle is 30 feet" means that L+M+S = 30
2. "The longest side is 1 foot longer than the medium side" means that L = M+1
3. "The shortest side is 7 feet shorter than the medium side" means that M = S+7

Now, replace S+7 for M in the second point above to get L = (S+7)+1 = S+8.

Next, we can replace L = S+8 and M = S+7 into the equation from point 1 above to get:

L+M+S = (S+8)+(S+7)+S = 30.

Simplifying gives us:

3S+15 = 30

3S = 15

S=5.

Now we can substitute into the equations from the paragraph above which gives:

L = S+8=5+8=13

M = S+7 = 5+7 = 12

So the longest side is 13 feet, the medium is 12 feet, and the shortest side is 5 feet.