Doubling the side
The obvious guess fails
A square with twice the side has 2 times 2, which is 4 times the area.
📚 Chapter Learning Kit
The Baudhāyana-Pythagoras Theorem · Class 8 Mathematics · Ganita Prakash
English 3 topics 105 leveled MCQs 51 flashcards 5 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
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Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
Build on the diagonal
Baudhayana’s one line
A square raised on the diagonal covers twice the ground of the one it came from.
Why the rule works
Count the triangles
East-west and north-south lines cut the original into two small triangles.
Two squares of one size
The easy case first
Two copies of a square combine into a larger square through the diagonal of either.
For squares of any sizes
Baudhayana’s rule
The square produced by the diagonal has the areas of the squares on the two sides together.
When the squares match
It agrees with the old case
Equal squares make the right triangle isosceles.
📖 Smart notes
What you'll study, topic by topic
1
Doubling a square, and the diagonal
A square built on the diagonal of another has exactly double its area. That single fact gives the hypotenuse of every isosceles right triangle, and it forces the arrival of a brand new kind of number.
- Doubling every side multiplies the area by four, not two.
- The square on the diagonal has double the area of the original.
- The original holds two small triangles and the new one holds four.
~35 min · full explanation, examples & memory tricks in the app
2
Combining two different squares
Two squares of any sizes can be joined into one. Stand their sides as the legs of a right triangle, and the square on the hypotenuse holds exactly the two areas together.
- Two equal squares combine through the diagonal of either.
- Two unequal squares need a right triangle built on their sides.
- The square on that hypotenuse holds both areas together.
~35 min · full explanation, examples & memory tricks in the app
3
Triples, Fermat, and applications
Some right triangles have whole-number sides, and those triples can be scaled and generated endlessly. The same question asked about cubes stayed open for 350 years.
- A triple of whole numbers with a squared plus b squared equal to c squared.
- Baudhayana listed six of them, beginning with 3, 4 and 5.
- Scaling every member by k gives another triple, since k squared factors out.
~40 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
105 questions laddered from warm-up to topper-level, each with an explanation. A taste:
Baudhayana asked how to build a square with twice the area of a given square, and a pupil who doubles every side instead produces a square with
Beginner
A twice the area
B four times the area
C eight times the area
D half the area
Show answer & explanation
four times the area
Two times two is four, so the area is quadrupled.
Baudhayana’s own answer says the side of the doubled square should be
Beginner
A twice the side of the original square
B one half of that same diagonal
C the perimeter of the original square
D the diagonal of the original square
Show answer & explanation
the diagonal of the original square
A square raised on the diagonal covers twice the ground.
Drawing east-west and north-south lines through the figure cuts the ORIGINAL square into
Intermediate
A four small congruent triangles
B eight small congruent triangles
C three small congruent triangles
D two small congruent triangles
Show answer & explanation
two small congruent triangles
A square falls into two triangles along a diagonal.
Those same lines cut the TILTED square standing on the diagonal into
Intermediate
A four small congruent triangles
B two small congruent triangles
C six small congruent triangles
D eight small congruent triangles
Show answer & explanation
four small congruent triangles
Four against two is what makes the area double.
🃏 Flashcards
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51 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
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Memory Match
Word Match
Categorization
Fact Or Myth
Sequence Builder
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