Answer
The answer is: two 42 ft sides and one 38 ft side.
Work Step by Step
We assign the variables:
x = length of each of the two equal sides
y = length of the third side
Step 1:
Find the equations that represent the problem.
The perimeter for an isosceles triangle can be calculated with the formula
$P=2x+y$
From the exercise we know the perimeter is 122 ft.
$2x+y=122$ -> Eq. 1
We can get the second equation from the wording in the problem.
From "The length of the third side is 4 ft shorter than either of the other two sides.", we get
$y=x-4$ -> Eq. 2
Step 2:
Solve the system of equations. Using the substitution method,
-> Substitute Eq. 2 into Eq. 1
$2x+x-4=122$
$3x=122+4$
$3x=126$
$x=\frac{126}{3}$
$x=42$
-> Substitute the value for x into Eq. 2
$y=42-4$
$y=38$
Step 3:
The answer is: two 42 ft sides and one 38 ft side.
