Yes, a triangle with side lengths 12, 16, and 20 is a right triangle. This is because these lengths satisfy the Pythagorean theorem.
Yes, a triangle with sides of lengths 12 ft, 16 ft, and 20 ft is a right triangle, as it satisfies the Pythagorean theorem. When applying the theorem, the squares of the two shorter sides add up to equal the square of the longest side.
The latter is a well known right triangle (Pythagorean 'triple').
The numbers that make up today's date—12, 16, and 20—form a Pythagorean triple. That is, 12² + 16² = 20².
∴ area of triangle = 96 cm2. Hence, the given triangle is a right-angled triangle.
It is satisfying the Pythagoras theorem, thus the given triangle is a right-angled triangle.
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
Here, we know that the standard form of the Pythagorean triplet is (2m, m2 – 1, m2 + 1). So the Pythagorean Triplet is 12,35,37.
Textbook & Expert-Verified⬈(opens in a new tab)
The triangle with side lengths 12, 16, and 20 is classified as a right triangle since it satisfies the Pythagorean theorem (12² + 16² = 20²).
Similarly to the twin prime conjecture, it is conjectured that there are infinitely many prime triplets. The first known gigantic prime triplet was found in 2008 by Norman Luhn and François Morain.
The theorem states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the right triangle. These three sides of the right triangle form the Pythagorean triples.
Not only is each number in today's date (9/16/25) a perfect square—their consecutive square roots are also an example of a Pythagorean triple. While an official name has yet to be assigned, “Pythagorean Triple Square Day” encapsulates the moment pretty perfectly.
Solution: A Pythagorean triplet consists of three positive integers a, b, and c, such that a2 + b2 = c2. 74 ≠ 81, so (5, 7, 9) is not a Pythagorean triplet.
Sin is equal to the side opposite the angle that you are conducting the functions on over the hypotenuse which is the longest side in the triangle. Cos is adjacent over hypotenuse. And tan is opposite over adjacent, which means tan is sin/cos.
We can also see that the 5, 12, 13 is a Pythagorean triplet, the other Pythagorean triplets are 3, 4, 5. This means that any triangle with sides of Pythagorean triplets is always a right angle triangle.
Expert-Verified Answer
Given that, Two sides of a triangle are 15 cm and 11 cm and its semiperimeter is 19 cm. Let assume that a, b, c, represents the three sides of a triangle such that a = 15 cm, b = 11cm. Hence, Measure of third side will be 12 cm.