Squares on a Right Triangle

In the picture

1. 1The brass angle marker lying in the triangle’s square corner, where the two short sides meet.
2. 2The small teal square, built on the shortest side of the triangle.
3. 3The mustard square, built on the other short side, the one that meets the teal square at the square corner.
4. 4The large coral square, built on the longest side, across from the square corner.

Examples

• A ladder leaning on a wall: the height on the wall and the distance of its feet from the wall give the ladder’s length.
• Walking 3 blocks east and then 4 blocks north leaves you exactly 5 blocks from where you started.

Quiz: Squares on a Right Triangle (Age 13)

1. 1

   A right triangle has a square built on each of its three sides. What is true about their areas?

   • The areas of the two smaller squares add up to the area of the largest square.
   • All three squares have the same area.
   • The area of the largest square is the two smaller areas multiplied together.
2. 2

   Squares are built on the two sides that meet at the right angle, and their areas are 9 and 16. What is the area of the square on the longest side?

   • 12
   • 25
   • 7
3. 3

   For which triangles does this rule about the squares' areas work?

   • Only triangles that contain a right angle.
   • Any triangle whose three sides all have different lengths.
   • Any triangle, as long as the squares are drawn on the outside.

The answers, each with its explanation, are in the app. This lesson has left the free week, so its quiz is part of the subscription.