a student has 6 pencils the lengths are 1523456 can he make

a student has 6 pencils. the lengths are 1.5,2,3,4,5,6 can he make a right triangle?draw the only possible right triangle.

Solution

We have the Pythagoras theorem which states that (Base)² + (height)² =(Hypotenuse)².

Yes, He can make a right triangle, with the pencils of length 3,4,5 where 5 is the hypotenuse and 3 and 4 can be the height and base. we get 3² + 4² = 25 = 5².

Such sets are called pythagorean triplets (other examples are (6,8,10), (5,12,13), (8,15,17) etc)