Question

Number 3 plzzzzzzzzz

Answer 1

Answer: A) 4

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For any triangle with sides a,b,c we can say that the third side c is bound by this restriction

b-a < c < b+a

where 'a' and 'b' are known values, and 'b' is the larger value. So in this case we know that a = 8 and b = 12 making this inequality

b-a < c < b+a

12-8 < c < 12+8

4 < c < 20

The unknown missing side is between 4 and 20, not including either endpoint. This means c cannot equal 4, and c cannot equal 20 either.

Since c = 4 is not possible, this points to choice A as the answer

The other values 12, 8 and 16 are all in the range from 4 to 20, so they are valid possible lengths for c.

note: I'm using the triangle inequality theorem

Answer 2

A

Explanation:

I'm pretty sure some smart guy in Greece noticed this but:

Since 4 + 8 = 12, thats the only option where 2 of the smaller sides add up to the big one. I don't know much of the reasoning behind this but my math teacher showed it to us by using Popsicle sticks to make triangles. You can try it if that helps you think about it. Apparently, if you add up the 2 smaller sides, then it HAS to be more than the biggest side.