Question

A person makes a triangular garden. The longest side of the triangular section is 7 feet shorter than twice the shortest side. The third side is 3 foot longer than the shortest side. The perimeter is 60 feet. How long is each side?

Answer 1

the "shortest side" is `16` feet long
the "longest side" is `25` feet long
the "third side" is `19` feet long

Explanation:

All the information given by the question is in reference to the "shortest side"
so let us make the "shortest side" be represented by the variable `s`

now, the longest side is "7 feet shorter than twice the shortest side"
if we break down this sentence,
"twice the shortest side" is 2 times the shortest side
that would get us: `2s`
then "7 feet shorter than" that would get us: `2s - 7`

next, we have that the third (last) side is "3 feet longer than the shortest side"
we can interpret this as the shortest side plug 3
which will get us: `s + 3`

then, the perimeter of a triangle is all the sides added up
we are told this is 60 feet
so we can make the equation:
`60 = (s) + (2s - 7) + (s+3)`

we can then add like terms
`60 = s + 2s - 7 + s + 3`
`60 = 4s - 4`

add 4 to both sides
`4s = 64`

then divide 4 from both sides
`s = 16`
this gives us that the "shortest side" is `16` feet long

if we plug this back in to find the longest side:
`2s - 7 = 2(16) - 7 = 32 - 7 = 25`
this gives us that the "longest side" is `25` feet long

and if we plug the shortest side into the third side
`s + 3 = 16 + 3 = 19`
this gives us that the "third side" is `19` feet long