SOLUTION: Please help! I have been stuck on it for a while. Thank you so much. One side of triangle is one-fourth the longest side. The third side is 7 feet less than the longest side. Th

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Question 926397: Please help! I have been stuck on it for a while. Thank you so much.
One side of triangle is one-fourth the longest side. The third side is 7 feet less than the longest side. The perimeter is 137. Find all three sides.
Found 3 solutions by TimothyLamb, brysca, MathTherapy:
Answer by TimothyLamb(4379)   (Show Source): You can put this solution on YOUR website!
x = longest side
y = second side
z = third side
--
y = x/4
z = x - 7
x + y + z = 137
---
put the system of linear equations into standard form
---
y = x/4
z = x - 7
x + y + z = 137
---
x - 4y = 0
x - z = 7
x + y + z = 137
---
copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
solution:
x = longest side = 64 ft
y = second side = 16 ft
z = third side = 57 ft
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
Answer by brysca(112)   (Show Source): You can put this solution on YOUR website!
solution posted below
.
hope this helps!
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Please help! I have been stuck on it for a while. Thank you so much.
One side of triangle is one-fourth the longest side. The third side is 7 feet less than the longest side. The perimeter is 137. Find all three sides.


Let the length of shortest side, be S

Then length of longest side = 4S, and length of 3rd side = 4S - 7

As the lengths sum to 137, we get: S + 4S + 4S - 7 = 137

9S - 7 = 137

9S = 144

S, or length of shortest side = , or  ft

Length of longest side: 4(16), or  ft

Length of 3rd side: 4(16) - 7, or 64 - 7, or  ft 

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