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?

1 Answer
Nov 30, 2015

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: 2s7

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)+(2s7)+(s+3)

we can then add like terms
60=s+2s7+s+3
60=4s4

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:
2s7=2(16)7=327=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