Pls. help me understand the question?And also to solve.?

Question

Two sides of a triangle are 8 and 5. The third side of the triangle is a whole no.How many possible lengths for the third side are there?

Answer 1

If you draw it out, you will find that the third side has to be at least 3, because if it was less than 3, you couldn't make a triangle at all. In fact, if the third side were 3 exactly, it wouldn't make a triangle either, just a straight line. (Because 8 - 5 = 3!)

So the third side must be 4 or more.

Then notice that the third side can't be 13 either, because you'd have another straight line (8 + 5 = 13).

So the third side must be 12 or less.

That means the possible lengths for the third side are:
4, 5, 6, 7, 8, 9, 10, 11, and 12.

Answer 2

You could think of it this way. Draw a line, 8 inches long. Now get a stick 5 inches long. Put one end of the stick at the end of the 8-inch line (maybe a thumb tack will keep it there.)

Now rotate the stick to various positions. At each position, imagine a third line, from the end of the stick to the other end of the line. The three line make a triangle.

If you line up the line and the stick close to each other, the 3rd line wil be 3 inches. And if you rotate the stick to the other side, as far away as it can go, the 3rd line will be 8 + 5 = 13 inches.

So the 3rd side of the triangle can be anything between 3 and 13 inches. That is, it can be 4, 5, 6, 7, 8, 9, 10, 11, or 12 inches. That's 9 possible lengths.

You can discuss with your teacher if the third side can be 3 inches, or 13 inches. That would make a triangle so flat that it would be just a straight line.

Answer 3

The third side can never be greater than or equal to the sum of the other two, nor can it be less than or equal to the difference. Therefore, the third side can be any number in the set:

{ 4, 5, 6, 7, 8, 9, 10, 11, 12 }

Answer 4

There are an infinite number of lengths, but since you are looking for integer lengths, the set would be c = third side such that:

3 < x < 13

so... 4, 5, 6, 7, 8, 9, 10, 11, 12

9 total possible whole number lengths for the third side.

Answer 5

Check out this thought experiment.

Pin the two pieces you have together at the end so that they can rotate.

Then starting with them in a straight line gives the largest third side: 8+5 = 13

Now rotate the short one around 180 degrees, this gives the shortest side = 8-5=3

Whole numbers between them are possible solutions.

Answer 6

U could use the Pythagreon Theorum like the fgal above me did and i highly recomend using it


C does not equal 9 by the way.



a2+b2=c2


a2=64+b2=25


64+25=89


so the c2= 9.4339811321


good luck with math kid

Answer 7

a squared + b squared = c squared (a2 + b2 = c2)

64 + 25 = 89

then find the square root of 89, which is 9 x 9 = 89

C = 9