Question

please help guys? stuck!

At the end of The Wizard of Oz, the Scarecrow earns his diploma. He then says, “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side”. How should this statement of the Pythagorean Theorem correctly read?

Answer 1

A. The sum of the squares of any two sides of a right triangle is equal to the square of the shortest side..
B. The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the largest side.
C. The difference of the squares of any two legs of a right triangle is equal to the square of the hypotenuse.
D. The sum of the squares of any two legs of a right triangle is equal to the square of the hypotenuse.

Answer 2

@jim_thompson5910

Answer 3

I got C as my answer. Is that right?

Answer 4

Let me rewrite what you chose, in mathematical symbols:

\[a^2 - b^2 = c^2\] or \[b^2 - a^2 = c^2\]
(difference = subtraction)

Does that agree with my splendid drawing?

Answer 5

yes

Answer 6

Think about what happens if those two legs are equal? What is the difference? Is that the length of the hypotenuse?

Answer 7

yes

Answer 8

If a = 1 and b = 1, the difference of the squares is 1^2 - 1^2 = ?

Answer 9

Again, "difference" means "subtract one from the other". The two legs in the right triangle are a and b. The "difference of the squares of any two legs of a right triangle" means a^2-b^2 or b^2-a^2. I hope you now realize that answer cannot possibly be correct...otherwise it must be the case that 1^2 -1^2 = 1 - 1 = 0 is the hypotenuse of a right triangle with legs 1 and 1. Could you draw that triangle for me, please? :-)

Answer 10

so then D would be our answer

Answer 11

Yes. The sum of the squares of the legs is the square of the hypotenuse. a^2+b^2=c^2