Find the lengths of each side
This word problem is about a triangle whose perimeter is 47 miles. Since it's asking to find the length of each side, then there are 3 unknowns. So here's what we do:
Let the variables S1 be the length of side 1 in miles,
S2 be the length of side 2 in miles,
and S3 be the length of side 3 in miles.
Now, the next thing to do with these variables is to set up equations that follow the word problem. Here they are as follows:
S1+S2+S3=47 the perimeter of the triangle by adding the lengths of all three sides
S1=(2*S2)-5 1st side (represented by S1) is (represented by =) 5 less (represented by -5) than twice the 2nd side (represented by 2*S2).
S3=S1+2 3rd side (represented by S3) is 2 more (represented by +2) than the 1st side.
Next, since we have more than one unknown, we should express one equation in terms of one variable. Since only one variable has a coefficient which is S2 in the term, 2*S2, I suggest that we express the other variable equations of S1 and S3 in terms of S2. Here's how it goes:
S1=(2*S2)-5 as S1 is already expressed in terms of S2
S3=S1+2=[(2*S2)-5]+2 I plugged in the S1 equation to express S3 in terms of S2.
=(2*S2)-5+2 I combined like terms.
Now that I have expressed both S1 and S3 in terms of S2, I can plug those equations into that for the triangle perimeter:
(2*S2)-5+S2+(2*S2)-3=47 Again, I combined like terms.
+8=+8 I added 8 on both sides of the equation to eliminate -8 on the left side.
S1=(2*11)-5=22-5=17 Now that I have found the value of S2, I can plug it into the S1 equation.
S3=17+2=19 Now that I have found the value of S1, I can plug it into the S3 equation.
So now here are the lengths of each side of the triangle. Side 1 is 17 miles, side 2 is 11 miles, and side 3 is 19 miles.