Question

A triangle has two sides of length 8.1 and 1.4. If the length of the third side is an even integer, what is it's length?

Answer 1

Are you told it is a right triangle?

Answer 2

I wish

Answer 3

We don't have to assume it is, but if it is a right triangle we can use the Pythagorean Theorem. If it is not, then we use facts about triangle lengths. What do you know about a third side of any triangle, in relationship to the other two sides?

Answer 4

I know the angles must add up to 180 degrees

Answer 5

There is a Theorem that states: Given any triangle, the sum of the lengths of any two sides of the triangle is greater than the length of the third side. So the length of the third side must always be less than the sum of the other two lengths.

Think of the concept of the shortest distance between two points is a straight line
so the length of the third side must be less than the sum of the other two sides and that will also need to hold true for all three pairs of sums



first, let's add the two sides we know
1.4 + 8.1 =

Answer 6

@daniel.ohearn1 what is 1.4 + 8.1 = ?

Answer 7

9.5

Answer 8

that means the other side must be less than 9. You are told the other side is an integer
so what are the possible lengths of the third side?

Answer 9

What are the integers less than 9.5 ?

Answer 10

2, 4, 6 or 8

Answer 11

those are even positive integers less than 9. Did the directions state the other side is an even integer?

Answer 12

Yes

Answer 13

Oh, wait it did. Sorry I misread that. You are correct.

Answer 14

now we check these to see if the pairs will work for all around the triangle
which number do you want to try firsy?

Answer 15

Ohh so it's 8

Answer 16

by ur same logic

Answer 17

if it is 8, then all pairs will need to be smaller than the third side
so we check the other two pairs. we checked 8 is less than 1.4 + 8.1
now we check the other two pairs

Answer 18

8.1 needs to be smaller than 1.4 + 8 and 1.4 needs to be smaller than 8.1 + 8

Answer 19

You can say that the missing side won't be smaller than 8.1-1.4

Answer 20

In order to have a triangle

Answer 21

True in this case, since the other side will need to be smaller than the other two sums
since all of these work, we found the other side
take a look at what happens if you pick one of the others....
let's look at 6... 6 is smaller than 1.4 + 8.1

Answer 22

Does that help now? :)

Answer 23

Yes, thanks for your help