SOLUTION: one side of a triangle is a. the second side is 4 more than half of a and the third side is 7 less than twice a. a. write an expression for the length of second side in terms of

Algebra ->  Triangles -> SOLUTION: one side of a triangle is a. the second side is 4 more than half of a and the third side is 7 less than twice a. a. write an expression for the length of second side in terms of       Log On


   

Question 99922: one side of a triangle is a. the second side is 4 more than half of a and the third side is 7 less than twice a.
a. write an expression for the length of second side in terms of a.
b. write an expression for the length of the third side in terms of a.
c. find the perimeter if a = 3
Found 2 solutions by checkley71, doukungfoo:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
a first side
a/2+4 second side
2a-7 third side
3+(3/2+4)+(2*3-7)
3+5.5+6-7
8.5-1=7.5 for the perimeter.
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Problem with this problem:
Side 3 (2*3-7)=(6-7)=-1 which is not a valid measurement for the side of a triangle.
The math works but this is a very bad problem & needs to be eliminated if it is a class problem because you can't construct or draw this triangle which is necessary in many math & geometry examples.
For this example to be valid the value of 'a' need to be > 3.5 for side 3 to have a positive length.

Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
write expression for length of second side in terms of a
Given: second side is 4 more than half of a
so the expression would be
SecondSide=4%2B%281%2F2%29a or
SecondSide=4%2Ba%2F2
next
write an expression for the length of the third side in terms of a
Given: the third side is 7 less than twice a
ThirdSide=2a-7
last
find the perimeter if a = 3
Known: perimeter of a triangle equals the sum of all its sides
perimeter=a%2B%284%2Ba%2F2%29%2B%282a-7%29
perimeter=3%2B%284%2B3%2F2%29%2B%282%283%29-7%29
perimeter=3%2B%284%2B1%261%2F2%29%2B%286-7%29
perimeter=3%2B5%261%2F2-1
perimeter=7%261%2F2 or
perimeter=7.5
Note: this is how the math works but with the given information a=3 there is a problem. If a=3 then the third side which is 2a-7 would result in the third side being -1. There can be no triangle with this measurement.