SOLUTION: A square animal pen and a pen shaped like an equilateral triangle have equal perimeters. find the length of the sides of each pen if the sides of the triangle pen are 8 less than t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A square animal pen and a pen shaped like an equilateral triangle have equal perimeters. find the length of the sides of each pen if the sides of the triangle pen are 8 less than t      Log On


   

Question 517042: A square animal pen and a pen shaped like an equilateral triangle have equal perimeters. find the length of the sides of each pen if the sides of the triangle pen are 8 less than twice the side of the square pen
Found 2 solutions by JBarnum, mananth:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
this looks like a fun problem
All we are given:
all sides of square are same length (s)
all sides of triagle are same length (t)
same perimeter (p) for both triangle and square
s%2Bs%2Bs%2Bs=p
4s=p
t%2Bt%2Bt=p
3t=p
4s=3t
t=2s-8
------------
use substitution method for t
4s=3%282s-8%29 distribute the 3
4s=6s-24 subtract 4s from both sides
0=2s-24 add 24 to both sides
24=2s divide by 2
highlight%2812=s%29
use substitution method for s
4%2812%29=3t multiply the 4 and 12
48=3t divide by 3
highlight%2819=t%29
-----------------
check
4%2812%29=3%2819%29
48=48
correct

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
length of side of square =x
length of side of triangle = 2x-8
...
perimeter of squale = 4L
perimeter of equilateral triangle = 3a
4L=3a
4x=3(2x-8)
4x=6x-24
-2x=-24
/-2
x=12 the side of square
side of triangle = 2x-8 => 2*12-8=>16