Question 554970: the perimeter of a triangle is 52 cm the longest side is 2 cm less than the sum of the other 2 sides twice the shortest side is 15 centimeters less than the longest side find the lengths of each side of the triangle
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let the triangle be have sides of a, b, and c
let p equal the perimeter.
p = a + b + c
p = 52 cm.
let a be the longest side.
since the longest side is equal to 2 less than the sum of the other 2 sides, you get:
a = b + c - 2
let c be the shortest side.
since 2 times the shortest side is equal to 5 less than the longest side, you get:
2c = a - 15
you have:
a + b + c = 52
a = b + c - 2
2c = a - 15
you can solve for b in terms of a and you can solve for c in terms of a.
then you'll have an equation for the perimeter that only has "a" in it which will allow you to solve for "a".
once you have solve for "a", you can then use the other equations to solve for b and c.
take a = b + c - 2
subtract c from both sides of the equation and add 2 to both sides of the equation to get:
a - c + 2 = b
this is the same as:
b = a - c + 2
take 2c = a - 15
divide both sides of this equation by 2 to get:
c = a/2 - 15/2
you now have 3 equations to work with.
they are:
p = a + b + c
b = a - c + 2
c = a/2 - 15/2
in the equation of:
b = a - c + 2
you can substitute for c to get:
b = a - c + 2 becomes:
b = a - (a/2 - 15/2) + 2
remove parentheses to get:
b = a - a/2 + 15/2 + 2
combine like terms to get:
b = a/2 + 19/2
you now have:
p = a + b + c
b = a/2 + 19/2
c = a/2 - 15/2
you can now subsitute for b and c in the equation of p = a + b + c to get:
p = a + a/2 + 19/2 + a/2 - 15/2
combine like terms to get:
p = 2a + 2
since p = 52, you get:
52 = 2a + 2
subtract 2 from both sides of this equation to get:
50 = 2a.
divide both sides of this equation by 2 to get:
a = 25.
from the equation b = a/2 + 19/2, you will get:
b = 25/2 + 19/2 which becomes:
b = 44/2 which becomes:
b = 22
from the equation c = a/2 - 15/2, you will get:
c = 25/2 - 15/2 which becomes:
c = 10/2 which becomes:
c = 5.
you now have:
a = 25
b = 22
c = 5
p = a + b + c = 25 + 22 + 5 = 25 + 27 = 52.
looks like it works out and that's your answer.
the longest side is 25 and the middle size is 22 and the shortest side is 5.
confirm by going back to the original problem statement.
it says:
the longest side is 2 cm less than the sum of the other 2 sides.
you get:
25 = 22 + 5 - 2 which becomes:
25 = 27 - 2 which becomes:
25 = 25 ***** longest side length is confirmed.
2 times the shortest side is 15 cm less than the longest side.
you get:
2*5 = 25 - 15 which become:
10 = 10 ***** shortest side is confirmed.
everything check out ok so the answer is confirmed as correct.
longest side is 25
middle side is 22
shortest side is 5
|
|
|
