8.02 Pythagorean triples
Determine whether the following are Pythagorean triples:
\left(5, 12, 13\right)
\left(12, 5, 13\right)
\left(8, 14, 18\right)
\left(9, 16, 25\right)
\left(300, 400, 500\right)
\left(9, 12, 15\right)
\left(15, 8, 17\right)
\left(\dfrac{1}{3}, \dfrac{1}{4}, \dfrac{1}{5}\right)
Complete the following Pythagorean triples:
⬚, 15, 17
7, ⬚, 25
28, ⬚, 53
14, 48, ⬚
Peter knows the two smallest numbers in a Pythagorean triple, which are 3 and 4. Find the number Peter needs to complete the triple.
Sean knows the two largest numbers in a Pythagorean triple, which are 41 and 40. Find the number Sean needs to complete the triple.
Given that the length of the hypotenuse of a right-angled triangle is 20, find the two other side lengths that would complete a Pythagorean triple.
Find the number that completes a Pythagorean triple given the following:
The two largest numbers are 100 and 96.
The two smallest numbers are 22 and 120.
If x, y, and z form a Pythagorean triple, will 3 x, 3 y and 3 z be a Pythagorean triple?
Determine whether the following triples of numbers represent the sides of right-angled triangles:
\left(2, 4, 6\right)
\left(5, 12, 13\right)
\left(6, 8, 13\right)
\left(3, 4, 5\right)
Identify the hypotenuse of the following triangles:
For each of the following triangles, let a and b represent the two shorter sides and c the length of the longest side:
Find a^{2} + b^{2}.
Find c^{2}.
Is the triangle a right-angled triangle?
Consider the following right-angled triangle:
Write the equation that can be constructed from the given information.
A right-angled triangle has side lengths x, y, and z. Will a triangle with side lengths of 5 x, 5 y and 5 z make a right-angled triangle as well?
Consider the right-angled triangle with sides \left(8, 15, 17\right).
Find the length of the side that is opposite the largest angle.
Find the lengths of the two sides that are next to the right angle.
Consider a right-angled triangle with shorter side lengths of 15 units and 36 units.
Find the length of the hypotenuse in the triangle.
The triple is a multiple of a common Pythagorean triple. Which one?
Consider a right-angled triangle with side length of 40 \text{ cm} and hypotenuse of 85 \text{ cm}.
Find the length of the unknown side in the triangle.
The triple is a multiple of a common Pythagorean triple. Which one?
Three towns Melba, Florey and Giralang are positioned as shown in the diagram:
Which two towns are furthest apart, assuming a direct route is taken?
A group of engineering students have made a triangle out of some wooden strips. They have made a triangle with sides lengths 20 \text{ m}, 48 \text{ m}, and 52 \text{ m}.
Is the triangle they make a right-angled triangle?
How many metres of wooden strips did they use to make the triangle?
Find the other right-angled triangles they could create using the exact same length of wooden strips.