What is the minimum and maximum whole number side length for △ABC with given side lengths of 9 cm and 11 cm? Please explain why

Step-by-step explanation:

We would assume that triangle ABC is a right angled triangle. This means that we can apply Pythagoras theorem in determining the unknown side length.

For the case of the minimum side length, we would assume that the unknown length, L is one of the shorter legs of the triangle. By applying Pythagoras theorem, it becomes

11² = 9² + L²

L² = 121 - 81 = 40

L = √40 = 6.32

For the case of the maximum side length, we would assume that the unknown length, L is one of the hypotenuse of the triangle. By applying Pythagoras theorem, it becomes

L² = 9² + 11²

L² = 81 + 121 = 202

L = √202 = 14.21

The minimum side length is 6.32 and the maximum side length is 14.21

We need to estimate how tall is, on average, one of these object, and then count how many would be in a 5 feet high stack.

For example, on Google you may see that "1.5 cubic foot boxes are the standard box, manufactured by most companies". So, we assume that a standard cardboard box is 1.5 feet tall.

So, if we set the equation

So, there would be between 3 and 4 cardboard boxes in a 5 feet tall stack.

Similarly, we can see that the average book is 9 inches tall. 9 inches are 0.75

feet, so we have

So, there would be between 6 and 7 books in a 5 feet tall stack.

The average brick is 75 millimeters tall, which means 0.25 feet tall. Again, we have

So, there would be 20 bricks in a 5 feet tall stack.

Finally, a coin is about 0.006 feet, which leads to

So, there would be between 833 and 834 coins in a 5 feet tall stack.