Understanding the Blob Pythagorean Theorem

A king consults his counsellor on dividing his land among his daughters. The counsellor explains concepts of scaling and similarity, and introduces the 'blob Pythagorean theorem' to solve the king's problem. The king learns that similar shapes maintain proportional areas, and the theorem applies universally to all similar shapes. The counsellor demonstrates the theorem using right-angled triangles, and the king reflects on the moral of the story.

What shape is the piece of land that the king decides to keep for himself?

• A circle

• A square

• A rectangle

• A right-angled triangle

What happens to the area of a shape if its dimensions are doubled?

• The area is doubled

• The area is tripled

• The area is quadrupled

• The area remains the same

According to the counsellor, what is essential for the Pythagorean theorem to apply?

• All angles must be acute

• One angle must be a right angle

• All sides must be equal

• The shape must be a square

What does the counsellor call the theorem that applies to similar blobs?

• Blob Scaling Theorem

• Blob Similarity Theorem

• Blob Pythagorean Theorem

• Blob Area Theorem

What is the key concept demonstrated with the right-angled triangles?

• The area of a triangle

• The similarity of triangles

• The sum of the angles in a triangle

• The sum of the areas of two smaller triangles equals the area of the larger triangle