Please help me solve this?

Question

If the shortest side of a triangle is x meters, and the other two sides are 3x- 1 and 2x + 4 meters. Write a polynomial P(x) that represents the perimeter and then evaluate the perimeter polynomial if x is 4 meters.

Answer 1

The perimeter is just p(x) = x + (3x -1) + (2x -4) = 6x +3 , for every x>0 such that x, 3x -1 and 2x + 4 satisfies the condition to be the sides of a triangle, that is, each side must be less then the sum of the other 2.

So, we must have
x < 5x + 3 => which holds for every x>0.
3x -1 < 2x + 4 => x <5
2x + 4 < 4x -1 => x > 2.5

Therefore, the perimeter is p(x) = 6x +3 for x in (2.5 , 5). For other values of x, we don't have a triangle. This is important to point out.

Since 4 is in (2.5 , 3), we do have a triagle and it's perimeter is p(4) = 6 * 4 + 3 = 27


And : -provided x, 3x -1 and

If x = 4, then the sides of the triangle are 4, 11 and 12. The important thing here is to check if this is possible. In any triangle, each side is less then the sum of the other 2. And we readily see this condtion is satisfied when x =4.

Therefore, the

Answer 2

sides: x, 3x-1, 2x+4
Add the 3 side lengths of a triangle to get it's perimeter.

In this case:
P(x) = x+(3x-1)+(2x+4)
simplify with like terms:
P(x) = 6x+3

When x = 4 meters...
sub 4 into your perimeter equation...
P=6(4)+3
27

When x = 4 meters, your perimeter is 27 meters

Answer 3

just add all the sides
x + 3x - 1 + 2x + 4 = P
P = 6x + 3 or 3 ( 2x + 1)

x=4 P = 24 + 3 or 27

Answer 4

perimeter=x+3x-1+2x+4=6x+3
if x=4 then perimeter=6*4+3=27 meters.

Answer 5

This really isn't as hard as it sounds.

First off, a perimiter is just the sum (addition) of all of the side lengths.

perimeter = x + (3x-1) + (2x+4)
let P(x) represent the perimeter
P(x) = 6x + 3
if x = 4
P(4) = 6*4 + 3 = 27 metres

Answer 6

P(x) = total length of all three sides
P(x) = x + 3x - 1 + 2x + 4
P(x) = 6x + 3

if x = 4
P(4) = 6*4 + 3
P(4) = 24 + 3 = 27 m

Answer 7

p(x)=(3x-1+2x+4+x)
or,p(x)=3(2x+1)
p(4)=3(2*4+1)=27