Final answer:
Using the Pythagorean theorem with the lengths of 9 blocks and 5 blocks for the two sides of the triangle, we calculate the hypotenuse to be approximately 10.3 blocks. After rounding to the nearest whole number, the length of the unknown side of the triangle is 10 inches.
Step-by-step explanation:
To find the length of the unknown side of the triangle, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If we let A and B represent the lengths of these two sides, and C represent the hypotenuse, the Pythagorean theorem can be written as:
A² + B² = C²
In this question, the lengths A and B are given as 9 blocks and 5 blocks. Substituting these values into the Pythagorean theorem, we get:
9 blocks² + 5 blocks² = C²
Which simplifies to:
81 + 25 = C²
106 = C²
Taking the square root of both sides gives us:
C = √106 ≈ 10.3 blocks
Thus, the hypotenuse of the triangle is approximately 10.3 blocks. Because we are asked to round to the nearest whole number, the length of the unknown side of the triangle is 10 inches.