Question

Can 5ft 9ft 14ft make a triangle?

Answer 1

Answer: No, those measurements cannot make a triangle

Why not? Because of the fact that the first two sides (5 and 9) add to 5+9 = 14, which is exactly as long as the third side. I recommend you using a ruler to measure out 5 inches, 9 inches and 14 inches. Mark all three as separate segments on a piece of paper. Then cut out those segments to form strips of paper with the given lengths. Then try to form a triangle. You'll find that it is impossible since the smaller segments combine perfectly to get the longest segment. Instead of a triangle, you'll only have a line segment forming.

As a rule, when you add any two sides of a triangle, they must add to something larger than the third side. The rule more formally is

For any triangle with sides a,b,c, the following three inequalities must hold true

• a+b > c
• a+c > b
• b+c > a

Answer 2

Any dimensions can make a triangle, however

this does not make a right angled triangle.

Explanation:

Determine the length of the hypotenuse of a right angle triangle with side lengths 5ft and 9ft by using the formula:

`a^2+b^2=c^2\\`

`√(a^2+b^2) = c`

`c=10.29`

This is not equal to 14ft.