Question

A student has four sticks of wood that measures 3 inches, 4 inches, 5 inches, and 6 inches.Can the student use any three of these sticks to make a right triangle? Explain why or why not.

Answer 1

Yes, the student can use three of these sticks to make a right triangle.

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 :

`(Base)^(2)  + (Perpendicular)^(2)   = (Hypotenuse)^(2)`

Now, here among all four sticks

`(3)^(2)  +(4)^(2)   = 9 + 16  = 25`

and
`25 = (5)^(2)`

So, there exists three sticks of length 3 in, 4 in and 5 inches which satisft Pythagoras Theorem , such that:

`(3)^(2)  + (4)^(2)   = (5)^(2)`

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.