Math word problem..help!

Question

Brad sees a right triangle whose hypotenuse has length a and whose sides have length b and c. When asked about the relationship among the three sides, he says "a²+b²=c²". How should you respond?

 

Answer 1

"Well, Brad, in the general equation for the Pythagorean Theorem (a²+b²=c²), the letter c denotes the hypotenuse.  The letters a and b refer to the two shorter sides (the hypotenuse is always the longest side).

 

What you should say when you see this picture is:

      b² + c² = a²

since the problem says, 'hypotenuse has length a' and 'sides have length b and c.' 

 

The letters in the picture are not the letters in the equation."

Answer 2

"Sorry, Brad, your hypotenuse is a, not c, so a² = b² + c²."

Answer 3

He needs to adjust his (classic) statement of the Pythagorean Theorem, by adjusting it to match the notation given in the problem.  

 

The problem gives the hypotenuse as "a" not "c".  So, in this case, because the problem designated the names of the sides he should recognize the Pythagorean Theorem as:

 

hypotenuse² = leg₁² + leg₂²

 

so, in this problem

 

a² = b² + c²

 

 

Answer 4

Hi Aj, you should explain to Brad the Pythagorean Theorem relates the two sides of a right triangle to the hypotenuse and not the hypotenuse and and one side to the other side. The correct format of the theorem based on the information given would be:

 

b² + c² = a²

 

Show Brad what the difference would be based on his equation and the correct equation.

 

Questions?