Question

For each pair of numbers, find a third whole number such that the three numbers form a Pythagorean triple. 13, 85​

Answer 1

To find a third whole number that forms a Pythagorean triple with 13 and 85, we can use the formula for generating Pythagorean triples:

a = m^2 - n^2
b = 2mn
c = m^2 + n^2

where a, b, and c are the three sides of a right triangle, and m and n are positive integers with m > n.

We know that 13 and 85 are already two sides of a right triangle, so we can use the Pythagorean theorem to find the third side:

c^2 = 85^2 + 13^2
c^2 = 7226
c ≈ 85.0

So the third number that forms a Pythagorean triple with 13 and 85 is approximately 85.

Answer 2

Answer: 84

Explanation:

The Pythagorean theorem is a^2 + b^2 = c^2. We can find the third number by squaring 85 (c) so that it is 7225 and subtracting it by 13^2 (a) giving us 7056. Now we just have to use our calculator for the square root which is our answer 84 (b).