In triangle ABC, AB=6 and AC=9.2. If BC is an integer, what is the smallest possible perimeter of the triangle?

Question

 I need all steps

Answer 1

The length of one side of a triangle,
let's say side AB,
is the distance from A to B along a straight line.
Of course, it is less than the total distance covered
first going from A to C, and then
going from C to B.
In other words,
the length of one side of a triangle,
is less than the sum of the lengths of the other two sides.

So if the longest side's length must be less than the sum of the lengths of the other two sides,

 

Step 1 would be  finding each side. Use what you know first. AB=6, and AC=9.2 which means that  a is one half of AB or 3.If A is 3 then to find out C you would take A from C and get 6.2 as C. To actually get the perimeter

use these Handy formulas:                                                             Perimeter+=+AB+%2B+BC+%2B+AC,          Area+=+AC%2ABD%2F2 (area+=+width%2Aheight%2F2).

 

We know that AC=9.2  and AB=6 so all we have to do is insert 2(B) multiplied by each side we know to be able to calculate the total perimeter:      6+2(3)+2(3)+6.2+2(3)+9.2=39.4

 

I did not note a unit of measurement ,but you would notate that at the end

Answer 2

All of the sides form a triangle.  The perimeter of a triangle is the sum of its sides.  In addition to this, the sum of the first two sides is greater than the third side.

 

Using the last fact, we can write an inequality to represent the sum of the first two sides.

 

AB + AC > BC

 

6 + 9.2 > BC

 

15.2 > BC

 

BC < 15.2

 

 

In order for the perimeter to be as small as possible, BC must be 1.  The smaller the side, the smaller the perimeter.

 

Perimeter = 6 + 9.2 + 1 = 16.2

 

 

If BC was equal to 15, then the perimeter would be

 

Perimeter = 6 + 9.2 + 15 = 30.2

 

 

We can see that BC=1 gives the smallest possible perimeter.

 

 

Note: Keep in mind that a side length of any figure can never be zero nor a negative value.

 

 

Answer 3

difference of two sides < BC < sum of two sides

(9.2 - 6) < BC < (9.2 + 6)

3.2 < BC < 15.2

If BC is an integer and the smallest possible perimeter, then BC = 4