Question

Sonya has four straws of different lengths: 2 cm, 8 cm, 14 cm, and 16 cm. How many triangles can she make using the straws? A no triangle B more than two triangles с one triangle two triangles

Answer 1

Note that in any triangle, The third side is always less than the sum of the two other sides and bigger than difference of the two other sides.

From these set of straws we have these possible triangles :

a. 2-8-14

b. 2-8-16

c. 2-14-16

d. 8-14-16

Let's take at look at a.

2-8-14

The sum of two sides is 2+8 = 10

Since 14 is NOT less than 10, and also 16 is NOT less than 10

You can't make a triangle with 2-8 straw.

So item a and b is disregarded

Let's look at c.

2-14-16

The sum of two sides is 2+14 = 16

Since 16 is NOT less than 16, You can't make a triangle with 2-14 straw.

So this is also disregarded.

The last one is d.

8-14-16

The sum of two sides is 8+14 = 22

The difference of two sides is 14-8 = 6

Since 16 is less than the sum which is 22

and

16 is greater than the difference which is 6

You can make a triangle with this set of straw

Therefore the correct answer is One Triangle