Question

converse of the pythagorean theorem (level 2)
score 25
possibly (500
question
the sides of a triangle are 78, 53, and 34. use the pythagorean theorem to determine if the
triangle is right, acute, or obtuse.
answer
attempt 1 out of 2
the triangle is
because the square of the largest side
the
sum of the squares of the other two sides.

Explanation:

Step1: Calculate the square of the largest side

$$78^2 = 6084$$

Step2: Calculate the sum of the squares of the other two sides

$$53^2+34^2=2809 + 1156=3965$$

Step3: Compare the two values

Since \(6084>3965\) (i.e., \(c^{2}>a^{2}+b^{2}\), where \(c = 78\), \(a = 53\), \(b = 34\))

Answer:

The triangle is obtuse because the square of the largest side (\(78^{2}=6084\)) is greater than the sum of the squares of the other two sides (\(53^{2}+34^{2}=3965\))