MathGrade 9ages 14–15
📐 3-4-5
Adding 3 and 4 to get 7 feels like the obvious move, but the Pythagorean rule works on areas, not lengths — and 3 and 4 squared, added and rooted, give 5.
Try this lesson freeNo card needed. The first lesson is free.
Download on the App StoreWhat your child learns
- The rule works only in a triangle with a right angle.
- The long side is the one facing the right angle, and it is always the longest.
- Add the squares of the two short sides and take the root, because the rule speaks about areas and not lengths.
- 3 and 4 give 5, and that is the triangle builders use to check a corner.
The mistake most kids make here
Adding the sides instead of their squares.
Try one question
In a right triangle the short sides are 3 and 4. What is the long side?
Short sides 3 and 4
- 5
- 7
- 12
Answer
5 — That's it. We added areas and then came back to a length.
How Maya teaches it
Your child tells Maya what they did in class. She teaches this topic at her desk, asks questions with tappable answers, and when the answer is wrong she explains why that answer was tempting instead of saying “try again”. She remembers what did not land and comes back to it.
Your child has it when they can: Say the long side of a triangle with sides 3 and 4.
How to help at home
The Pythagorean relationship only holds for the two short sides and the long side of a right triangle, and it works through squares, not straight addition — which is exactly the part that gets skipped.
Builders actually use the 3-4-5 triangle to check that a corner is truly square. Measure 3 units along one wall and 4 units along the perpendicular wall, mark both points, and measure the distance between the marks — it should come out to 5.
If your child adds 3 + 4 and expects 7 for the long side, say: "this rule is about the squares of the sides, not the sides themselves — 3 squared is 9, 4 squared is 16, and 9 plus 16 is 25, whose square root is 5. That's why builders trust 3-4-5, not 3-4-7."
A sign they've got it: given two short sides of a right triangle, they square each one, add the squares, and then take the square root — narrating each step rather than jumping straight to a guessed sum.
Questions parents ask
- Why doesn't 3 + 4 equal the long side of a right triangle?
- The Pythagorean rule relates the squares of the sides, not the sides themselves: 3 squared plus 4 squared equals 25, and the square root of 25 is 5 — the actual long side.
- What is the rule actually called, and when does it apply?
- It's the Pythagorean theorem, and it only applies to a right triangle — one with a 90-degree angle. The long side, opposite that angle, is called the hypotenuse and is always the longest side.
- Why do builders use a 3-4-5 triangle to check corners?
- If two walls measured 3 and 4 units from a corner are exactly 5 units apart, the corner must be a true right angle — a quick way to check squareness without special tools.
- How does Maya teach the Pythagorean theorem?
- Maya has the child square each short side, add the squares, and take the root step by step, using the 3-4-5 triangle builders actually use, before moving to other side lengths.
No card needed. The first lesson is free.
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