the lengths of two sides of a triangle are 6 cm and 3 cm. which could be the length of the third side?

Question

There are answer choices A. 12 cm B. 9cm C. 5cm D. 1 cm
If you can please, provide work =)

Answer 1

C.

All the others are impossible, because in all those cases one side is longer than (or equally long as) the sum of the other two sides, with is impossible.

Edit: And Nairbgnik, it is not really fair to first write some spam and later editing your post, only to get the first post.

Answer 2

The 3rd side of your triangle must satisfy the inequality:

3
So any answer between but not including 3 and 9 is possible. Of your answers only 5 satisfies that condition.

Too bad Yahoo answers does not allow diagrams. It would be so much easier to see why the answer is 5.

Lay the 6 and 3 cm sides end to end in a straight line. Lift one side up the tiniest bit. This makes the 3rd side almost 9, but not quite 9. Lay that side down the tinest bit and the 3rd side approaches 9 and becomes 9 when the sides are laying in a straight line, but then you no longer have a triangle. That's why the 3rd side must be less than but not equal to 9.

Now bring one side up and over until it approaches the other side and is almost laying in top of it. The 3rd side gets smaller and smaller and approaches 3cm in length. When the 2 sides are finally laying on top of one another the 3rd side becomes 3cm in length, but then you no longer have a triangle. You have one line on top of the other. So the 3rd side is always a little more than 3 and a little less than 9, or:

3
VOILA!

Answer 3

you are able to draw it, notwithstanding it should be very flat. really, on the grounds that a million+2 = 3 it really is a line section 3 instruments lengthy with yet another line section 3 instruments lengthy laying precisely on correct of it. That 2d line section should be both aspects a million unit and a pair of instruments lengthy strung out in a immediately line section 3 instruments lengthy. no longer what i should be prepared to call a triangle. some individuals would call it a "degenerate triangle".

Answer 4

There's not enough information... I will go on assuming this is a rectangle triangle, meaning that 2 of its sides conform a 90 degree angle.

By Pythagorean theorem...

a^2 + b^2 = c^2

So...

(6)^2 + (3)^2 = c^2
36 + 9 = c^2
45 = c^2

We get the square root of 45...

c = sqrt(45)
c = 6.7

So... neither of your answers matches this one meaning that it is not a rectangle triangle.

What kinf of triangle is it?

Answer 5

3
So any answer between but not including 3 and 9 is possible. Of your answers only 5 satisfies that condition.

Answer 6

A. Incorrect 6cm + 3cm < 12cm
B. Incorrect 6cm +3cm = 9cm
C. Correct because 3cm + 5cm = 8cm > 6cm (checking that the sum of the length of the shorter sides is smaller than that of the longest one is enough).
D. Incorrect 1cm + 3cm < 6cm

Answer 7

alright here we go, the formula to find this answer is Asquared + Bsquare = C squared
sooooo
6square + 3squared = Csq.
36 + 9 = Csq.
45=Csq.
Square root 45 and you get the answer, don't have a calculator on me so I dunno
oh and what sides of the triangle are those measures on cause that could change the answer as well

Answer 8

well the answer must be above 3 and under 9 because there cannot be one side that is bigger than the other two sides combined so it must be

C. 5 CM

Answer 9

By the triangle inequality theorem, any two sides must add up to more then the third side; therefore, the only one of your choices that works is C.

Answer 10

C

The sum of the two shorter sides must be larger then the length of the longest side