SOLUTION: The first side of a triangle is 7 cm shorter than twice the second side. The third side is 4 cm longer than the first side. The perimeter is 80 cm. Find the length of each side.

Algebra ->  Rectangles -> SOLUTION: The first side of a triangle is 7 cm shorter than twice the second side. The third side is 4 cm longer than the first side. The perimeter is 80 cm. Find the length of each side.      Log On


   

Question 338833: The first side of a triangle is 7 cm shorter than twice the second side. The third side is 4 cm longer than the first side. The perimeter is 80 cm. Find the length of each side.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let a, b, c = lengths of the 1st, 2nd and 3rd sides respectively
:
Write an equation for each statement, put in terms of a:
:
"The first side of a triangle is 7 cm shorter than twice the second side."
a = 2b - 7
2b = a + 7
b = %28%28a%2B7%29%29%2F2
:
"The third side is 4 cm longer than the first side."
c = a + 4
:
The perimeter is 80 cm.
a + b + c = 80
Replace b & c using the above equations
a + %28%28a%2B7%29%29%2F2 + (a+4) = 80
get rid of that annoying fraction, multiply by 2, results
2a + (a+7) + 2(a+4) = 2(80)
2a + a + 7 + 2a + 8 = 160
5a + 15 = 160
5a = 160 - 15
5a = 145
a = 145%2F5
a = 29 is side a
then
b = %28%2829%2B7%29%29%2F2
b = %28%2836%29%29%2F2
b = 18 is side b
and
c = 29 + 4
c = 33 is side c
:
:
See if those add up to 80
29 + 18 + 33 = 80