Final answer:
The Pythagorean theorem is applied to find the hypotenuse of a right triangle with sides 9 blocks and 5 blocks long, resulting in a straight-line path distance of approximately 10.3 blocks.
Step-by-step explanation:
To find the length of the hypotenuse of a right-angled triangle, we apply the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This can be represented by the formula a² + b² = c². In this example, if the lengths of the two sides of the triangle are 9 blocks and 5 blocks respectively, we can calculate the hypotenuse as follows:
First, square the lengths of the two sides: (9 blocks)² + (5 blocks)² = 81 + 25.
Next, sum these squares: 81 + 25 = 106.
Finally, take the square root of this sum to find the length of the hypotenuse: √106 ≈ 10.3 blocks, which is the straight-line path distance.
It's important to note that although '9' and '5' only have one visible significant digit, they actually represent discrete numbers, meaning '9 blocks' can be treated as '9.0' or '9.00 blocks' allowing us to state our result to a precision of three significant figures.