Answer:
Yes, the student can use three of these sticks to make a right triangle.
Step-by-step explanation:
The measure of four sticks = 3 inches, 4 inches, 5 inches and 6 inches.
Now, in a right angled triangle, by PYTHAGORAS THEOREM the three sides of the triangle base, perpendicular and hypotenuse are in the given following relation :
[tex](Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}[/tex]
Now, here among all four sticks
[tex](3)^{2} +(4)^{2} = 9 + 16 = 25[/tex]
and [tex]25 = (5)^{2}[/tex]
So, there exists three sticks of length 3 in, 4 in and 5 inches which satisft Pythagoras Theorem , such that:
[tex](3)^{2} + (4)^{2} = (5)^{2}[/tex]
So, the required length sticks are 3 inches, 4 inches and 5 inches.
Hence, the student use three of these sticks to make a right triangle.
