The sides of a triangle which are in arithmetic progression are 3x+1,3x+3,3x+5.Find the sides?

Answer 1

Put any value of x and you get the sides
there are infinite number of answers

Answer 2

You need more information. Is this a right triangle? If so, then by the Pythagorean Theorem we have
(3x + 1)^2 + (3x + 3)^2 = (3x + 5)^2. From this we find
9x^2 + 6x + 1 + 9x^2 + 18 x + 9 = 9x^2 +30x + 25 or
9x^2 - 6x - 15 = 0. We factor the left side and get
(3x - 5)(3x + 3) = 0. Of the two roots, x = 5/3 and x = -1, the latter is extraneous. Therefore, x = 5/3 and the sides are
6, 8, and 10.

Answer 3

If we have a triangle with sides a, b and c and c is the biggest of the tree then the only condition we have is that:

a+b > c (because the straight line is the shortest line between 2 points)

In this case the biggest line is 3x+5

So we have:

3x+1 + 3x+3 > 3x+5
6x+4 > 3x+5
3x>1
x>1/3

So the sides are any three numbers 3x+1, 3x+3, 3x+5 that have x>1/3

x>1/3 => 3x > 1 => 3x+1>2

So the sides are:
m, m+2, m+4 with m>2

Answer 4

Well, there is a rule that two sides cannot add up to be shorter than the third, so you could set up a system of inequalities to determine this.

3x+1 + 3x+3 > 3x+5
3x+1 + 3x+5 > 3x+3
3x+3 + 3x+5 > 3x+1

Combining like terms:
6x + 4 > 3x + 5
6x + 6 > 3x + 3
6x + 8 > 3x + 1

Moving terms around
3x > 1
3x > -3
3x > -7

And finally:
x > 1/3
x > -1
x > -7/3

So any number greater than 1/3 should do the trick.

Answer 5

I assume you mean that this is a right-angled triangle, and in that case we can use Pythagoras's theorem (a^2 + b^2 = c^2)to set the problem out as:
(3x+1)^2 + (3x+3)^2 = (3x+5)^2

Expand both sides:
(9x^2 + 6x + 1) + (9x^2 + 18x + 9) = (9x^2 + 30x + 25)

Collect like terms to get:
9x^2 - 6x -15 = 0

Factorise (or use quadratic formula):
3 (3x - 5) (x + 1) = 0

x = -1 or 5/3

It is easy to see that if x = -1 the traiangle cannot exist, so the only possibility is x = 5/3 which gives sides of 6, 8 and 10.

Answer 6

use pythagoras theorem,
a^2 + b^2 = c^2
(3x+1)^2 + (3x+3)^2 = (3x+5)^2
9x^2 + 6x + 1 + 9x^2 + 18x + 9 = 9x^2 +30x + 25
9x^2 - 6x -15 = 0
if you solve for x you will get
x = -1 or x = 15/9
since the side of the triangle cannot be negative, then the answer is, x = 15/9
so the sides are:
3(15/9) +1= 6
3(15/9) + 3 = 8
3(15/9) + 5 = 10