# Can you construct a triangle that has side lengths 2 in., 3 in., and 6 in.?

Dec 12, 2017

See an explanation below:

#### Explanation:

No, a triangle cannot be constructed with sides of 2 in., 3 in., and 6 in.

For three line segments to be able to form any triangle you must be able to take any two sides, add their length and this sum be greater than the remaining side.

$2 \text{in." + 3"in." = 5"in.}$

$5 \text{in." < 6"in.}$

For a triangle with sides 3 in., 4 in. and 5 in. which can form a triangle:

• 3 + 4 = 7 which is greater than 5
• 3 + 5 = 8 which is greater than 4
• 4 + 5 = 9 which is greater than 3

The shows the 2 and 3 inch line segments at a ${180}^{o}$ angle. There is no angle you can put the 2 and 3 inch line segment at which will allow it to be 6 in. long.