#### Question

# Math question need help!?

two sides of a triangle each have length 5. All of the following could be the length of the third side EXCEPT

a 1

b 3

c 4

d sqrt(50) (approximately 7.07)

e 10

pls, show me how you get the correct one.

#### Answer

The third side cannot equal 10. So the correct answer is e.

The reason is that for any triangle with sides a, b and c, the following must be true:

a+b>c

a+c>b

b+c>a

Since two of the sides of 5 then the other side must satisfy: 5 + 5 > other side

So other side must be < 10

except e, that would essentially give you two parallel lines, one on top the other, not a triangle

the angle between your 5 length sides would spread out to 180 deg, by definition not a triangle any more

E)10 because it is impossible for the third side to be two times the other two sides.

what to do:

1 inch= lenght of 5

2 inch= length of 10

use a ruler and try to see if it actually possible

good luck :)

The length of the third side of a triangle must be greater than the difference in length of the other two sides and less than the sum of the lengths of the other two sides.

If two of the sides have length 5, then the third side must be greater than 5-5 = 0 and less than 5+5 = 10.

All of the choices fall within that range except e 10. 10 is greater than 0, but 10 is not less than 10. Therefore, the only one of the choices that cannot be the third side is:

e 10

e. 10.

To find out if the lenghts could be the third side, just use the inequality a+b>c, where a is the first shortest side, b is the second shortest side, and c is the longest side. Since all of the values except one above fit this inequality, they are the possible lenghts of the third side. However a lenght of 10 does not fit this inequality, and therefore is not the third side of the triangle. This is becuase when you add 5 to 5 the shortest sides, you get a sum of 10 which is equal to 10, which does not fit the inequality since the sum of the shortest sides (5 and 5) must be greater not equal to the longest side (10). In conclusion 10 is not a possible lenght of the third side.