Answer:
A triangle with sides of length 11ft, 21ft, and 16ft is not a right triangle.
Explanation:
The Pythagorean theorem says that for any right triangle, the side lengths should fit this equation:
a² + b² = c²
where c is the hypotenuse of the triangle (hypotenuse = the longest side), and a, b are the other sides of the triangle.
If any triangle is a right triangle, the Pythagorean theorem will always work. So, to figure out if a triangle with sides of length 11ft, 21ft, and 16ft is a right triangle, we just need to see if the pythagorean theorem works:
a² + b² = c²
(c is the longest side, so c must be 21. The order of the other 2 sides ( a and b) don't matter).
11² + 16² = 21²
Now, we need to determine if the equation above is true or not. So, we can simplify it by getting rid of the exponents. (11² = 121, 16² = 256 , 21² = 441)
121 + 256 = 441
(simplify more by addition)
377 = 441
We have simplified this equation as much as we can. So, is it true? No. 337 does not equal 441, they are two different numbers. The pythagorean theorem did not work.
Because the pythagorean theorem did not work for the sides of this triangle, we can say that this triangle is not a right triangle.
Let me know if you have any questions!