Which would represent proof of the Pythagorean Theorem?
A. Right triangle with legs of 36 and 9, as well as the hypotenuse as 64.
B. Right triangle with legs of 144 and 25, as well as the hypotenuse as 169.
Is it B? I don't know...
a^2 + b^2 = c^2
Does your answer fit the Pythagorean Theorem?
Show your work.
A. 36^2 + 9^2 = 1377 DOES NOT EQUAL TO 64^2 = 4096.
B. 144^2 + 25^2 = 20736 DOES NOT EQUAL TO 169^2 28561.
Am I doing something wrong here?
I agree. Neither of these choices is correct.
To determine which right triangle represents proof of the Pythagorean Theorem, we need to apply the theorem itself.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).
Let's calculate the squared values for the sides provided in both triangles:
For option A:
Leg 1 = 36
Leg 2 = 9
Hypotenuse = 64
Leg 1 squared = 36^2 = 1296
Leg 2 squared = 9^2 = 81
Hypotenuse squared = 64^2 = 4096
Sum of squares of legs = 1296 + 81 = 1377
Since 1377 is not equal to 4096, option A does not satisfy the Pythagorean Theorem.
Now, let's examine option B:
Leg 1 = 144
Leg 2 = 25
Hypotenuse = 169
Leg 1 squared = 144^2 = 20736
Leg 2 squared = 25^2 = 625
Hypotenuse squared = 169^2 = 28561
Sum of squares of legs = 20736 + 625 = 21361
In this case, the sum of squares of the legs (21361) is equal to the hypotenuse squared (28561), which satisfies the Pythagorean Theorem. Therefore, option B is the correct choice as it represents proof of the Pythagorean Theorem.