Answer:
Missing side = 15
Yes. The side lengths 39, 36, and 15 form a Pythagorean triple.
Explanation:
Value of missing side:
Because this is a right triangle, we can find the missing side using the Pythagorean theorem, which is
a^2 + b^2 = c^2, where
- a and b are the shorter sides, called legs,
- and c is the longest side, called the hypotenuse (always opposite the right angle).
Thus, we can plug in 36 for a and 39 for c, allowing us to solve for b, the value of the missing side:
36^2 + b^2 = 39^2
1296 + b^2 = 1521
b^2 = 225
b = 15
Pythagorean triple question:
The numbers 39, 36, and 15 are Pythagorean triples:
- A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the legs (a and b) equals the square of the hypotenuse (c).
Since 36^2 + 15^2 = 39^2, the three numbers are a Pythagorean triple. You can see it better when we simplify:
36^2 + 15^2 = 39^2
1296 + 225 = 1521
1521 = 1521