Build a square on every side of a right triangle and watch the two small squares add up to the big one. Hunt for whole-number triples, solve ladder puzzles and beat the clock.
Start here. A square number is a number times itself: 3 × 3 = 9, 4 × 4 = 16, 5 × 5 = 25. A square with sides of 3 is made of 9 little squares. The square root goes the other way: the square root of 25 is 5, because 5 × 5 = 25.
The right triangle. A right triangle has one perfect square corner, called a right angle. The two short sides next to it are the legs. The long side opposite the right angle is the hypotenuse. It is always the longest side.
The big idea. Build a square on each side of a right triangle. The area of the square on the hypotenuse equals the two other squares added together. For legs 3 and 4: 9 + 16 = 25, so the hypotenuse is 5. In short: a² + b² = c². This is the Pythagorean theorem.
Finding a side. To find the hypotenuse, add the squares of the legs and take the square root. To find a missing leg, take the small square away from the big square: b² = c² − a², then take the square root. Ladders against a wall and the diagonal of a screen are right triangles in disguise.
Triples. Sets of whole numbers that fit, such as 3-4-5, 5-12-13 and 8-15-17, are called Pythagorean triples. Double or triple a triple and you get another one: 6-8-10, 9-12-15. Check any three sides: if the two smaller squares add up to the biggest square, the triangle is a right triangle.
Not a whole number. Legs of 4 and 6 give c² = 52. Since 7 × 7 = 49 and 8 × 8 = 64, the hypotenuse is between 7 and 8.
In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². It only works for right triangles.
The hypotenuse is the side opposite the right angle. It does not touch the little square that marks the right angle, and it is the longest side.
Three whole numbers a, b and c with a² + b² = c². The smallest is 3, 4, 5 because 9 + 16 = 25. Others are 5-12-13, 8-15-17 and 7-24-25.
Square the two shorter sides and add them. If the total equals the square of the longest side, it is a right triangle. For 5, 12, 13: 25 + 144 = 169 = 13 × 13, so yes.
Just starting: square numbers, square roots and squares on the sides. I know the basics: find the hypotenuse or a missing side. Challenge me: test for right triangles, ladder and diagonal stories, and square roots between whole numbers.
No. It is free and needs no account. Your stars are saved in your own browser.