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

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 :

$(Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}$

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.