Final answer:
The length of the hypotenuse of a right triangle with legs of 9 and 5 blocks is approximately 10.3 blocks, using the Pythagorean theorem and three significant figures for precision.
Step-by-step explanation:
Approximating the Length of the Hypotenuse
To approximate the length of the hypotenuse of the right triangle without using a calculator, we can apply the Pythagorean theorem which is defined by the formula c = √(a² + b²). For a right triangle with one leg of length 9 blocks and another leg of length 5 blocks, the formula becomes c = √(9² + 5²). Therefore, the length of the hypotenuse is c = √(81 + 25) which simplifies to c = √106. This is approximately 10.3 blocks when we use three significant figures to express the number more precisely, as mentioned in the provided information.