The question states that the three sides of the triangle, let's call them A, B, and C, equal 44 in. So we can use the equation:
a+b+c= 44in
The question states that the second side (b) is 2 inches more than twice the first side (a). So using this information, we can say:
2a+2=b
Following that statement, it is mentioned that the third side (c) is 12 inches less than three times the first side. We can then state:
3a-12=c
We can put these equations together inside the first equation stated by substituting each variable, so that now we have:
a+(2a+2)+(3a-12)=44
We then can combine like terms by combining all of the a values on the left side, so then the equation looks like:
6a-10=44
We got 10 from combining 2 and -12. After that, we can move 10 to the other side by adding 10, so our equation looks like:
6a=54
Finally, we divide by 6 on both sides to get the variable by itself, resulting in:
a=9
We now have the length of the first side, and we can plug this number in to the other two equations. Let's start with the second side, b.
2(9)+2
18+2
b=20
And then we will do the same thing for the third side, c.
3(9)-12
27-12
c=15
After plugging in for all three equations, we can finally answer the question:
First side (a)= 9in
Second side (b)= 20in
Third side (c) = 15in
We can double check by adding all three lengths together to make sure it equals 44:
9+20+15=44
29+15=44
44=44
