SOLUTION: I'm lost with this question. Can you help? One side of a triangle is 2/3rds as long as the second side and the second side is 2/3rds as long as the third side. The perimeter = 9

Algebra ->  Equations -> SOLUTION: I'm lost with this question. Can you help? One side of a triangle is 2/3rds as long as the second side and the second side is 2/3rds as long as the third side. The perimeter = 9      Log On


   

Question 70769: I'm lost with this question. Can you help?
One side of a triangle is 2/3rds as long as the second side and the second side is 2/3rds as long as the third side. The perimeter = 95cm. What is the length of the longest side?
Would the equation be:
95 = X + (X x 2/3) + (X x 2/3)2/3
Is X the longest side and how do I find X?
Found 2 solutions by checkley75, bucky:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
S1=2/3*S2
S2=2/3*S3
S1+S2+S3=95
2/3*S2+2/3*S3+S3=95
2/3(2/3*S3)+2/3*S3+S3=95
4/9*S3+2/3*S3+S3=95
(4*S3)/9+(2*S3)/3+S3=95
(4*S3+2*3*S3+9*S3)/9=95
(4S3+6S3+9S3)/9=95 ADD THE LEFT HAND TERMS & CROSS MULTIPLY
19S3=855
S3=855/19
S3=45 RDS. FOR THE THIRD (LONGEST) SIDE.


Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
My apologies. For some reason this answer became scrambled when I posted it, and I'm having a difficult time getting it corrected. Until I do, maybe you can sort your way through it and get enough of a clue to work it out. The error starts just after the line about dividing 95 by 19/5. Sorry for the mix up.
Your equation will work, it's just the algebraic manipulations that are hanging you up.
So let's go through the steps to crank out the answer.
.
X+%2B+%28X+%2A+2%2F3%29+%2B+%28X+%2A+2%2F3%29%2A%282%2F3%29+=+95
.
Let's multiply out the third term on the left side. By arithmetic rules when you multiply
two fractions you multiply their numerators and denominators. So 2%2F3%2A2%2F3+=+4%2F9
and the third term becomes %28X%2A4%29%2F9%29. This makes the equation become:
.
X+%2B+%28X+%2A+2%2F3%29+%2B+%28X%2A4%29%2F9+=+95
.
But before we can add the terms on the left side, we need a common denominator. You can
see that 9 would be a common denominator because 3 is a factor of it. So let's multiply the
first term on the left by 9%2F9 and the second term on the left by 3%2F3.
[This in effect is multiplying each of the terms by 1.] We don't have to do anything to
the third term because it already has the common denominator of 9. After these manipulations
the equation becomes:
.
9%2AX%2F9+%2B+6%2AX%2F9+%2B+4%2AX%2F9+=+95
.
Because the three terms on the left side have a common denominator, you can combine them
by adding the numerators and placing the sum over the common denominator. If you add
the numerators the result is 9%2AX+%2B+6%2AX+%2B+4%2AX+=+19%2AX. When you place this result over
the common denominator you get:
.
.
This division causes the left side to become just X.
For dividing the 95 by 19/5 use the rule that to divide by a fraction invert it and multiply.
.
So 95 divided by 19%2F9 is the same as 95+%2A+%289%2F19.
Note that 19 goes into 95 5 times so the answer to this division is 5*9 = 45.
.
The answer to this problem is that the long side is 45. If you back solve using this answer
you will find that the other two sides are 30 and 20 and the three sides do add up to 95.
.
Hope this helps.