Multiple Choice Identify the choice that best completes the statement or answers the question. 8. The length of the hypotenuse of a right triangle with legs measuring $6 \mathrm{~cm}$ and $8 \mathrm{~cm}$ is (a.) $10 \mathrm{~cm}$ b. $14 \mathrm{~cm}$ c. $48 \mathrm{~cm}$ d. $100 \mathrm{~cm}$ 9. The length of the hypotenuse of a right triangle with legs measuring $5 \mathrm{~m}$ and $12 \mathrm{~m}$ is a. $169 \mathrm{~m}$ b. $60 \mathrm{~m}$ c. $17 \mathrm{~m}$ (d.) $13 \mathrm{~m}$ 10. The lengths of the legs of a right triangle are $7 \mathrm{~cm}$ and $16 \mathrm{~cm}$. The length of the hypotenuse, to the nearest tenth of a centimetre, is a. $4.8 \mathrm{~cm}$ (b.) $17.5 \mathrm{~cm}$ c. $23.0 \mathrm{~cm}$ d. $305.0 \mathrm{~cm}$ 11. The lengths of the legs of a right triangle are $14 \mathrm{in}$. and $20 \mathrm{in}$. The length of the hypotenuse, to the nearest tenth of an inch, is a. 596.0 in. b. $34.0 \mathrm{in}$. (c.) $24.4 \mathrm{in}$ d. $5.8 \mathrm{in}$. 12. A chessboard measures $30 \mathrm{~cm}$ by $30 \mathrm{~cm}$. What is the length of the diagonal across the board, to the nearest centimetre? a. $8 \mathrm{~cm}$ (c) $42 \mathrm{~cm}$ b. $30 \mathrm{~cm}$ d. $60 \mathrm{~cm}$ 13. The mail slot in a door measures $12 \mathrm{~cm}$ by $2.5 \mathrm{~cm}$. Which of the following envelope sizes will fit through the opening without bending? a. $12.5 \mathrm{~cm} \times 18 \mathrm{~cm}$ c. $\quad 12.8 \mathrm{~cm} \times 20 \mathrm{~cm}$ b. $\quad 13 \mathrm{~cm} \times 16 \mathrm{~cm}$ (d) $12.2 \mathrm{~cm} \times 15 \mathrm{~cm}$
Solution
Step 1 ：Calculate the hypotenuse length for each right triangle using the Pythagorean theorem: \(\text{hypotenuse} = \sqrt{\text{leg}_1^2 + \text{leg}_2^2}\)
Step 2 ：Compare the calculated hypotenuse length with the given options to find the correct answer
Step 3 ：\(\text{hypotenuse}_8 = 10.0\)
Step 4 ：\(\text{hypotenuse}_9 = 13.0\)
Step 5 ：\(\text{hypotenuse}_{10} = 17.46424919657298\)
Step 6 ：\(\text{hypotenuse}_{11} = 24.413111231467404\)
Step 7 ：\(\text{hypotenuse}_{12} = 42.42640687119285\)
Step 8 ：\(\text{hypotenuse}_{13} = 12.257650672131263\)
Step 9 ：Final Answer:
Step 10 ：8. \(\boxed{10 \mathrm{~cm}}\)
Step 11 ：9. \(\boxed{13 \mathrm{~m}}\)
Step 12 ：10. \(\boxed{17.5 \mathrm{~cm}}\) (rounded to the nearest tenth)
Step 13 ：11. \(\boxed{24.4 \mathrm{~in}}\) (rounded to the nearest tenth)
Step 14 ：12. \(\boxed{42 \mathrm{~cm}}\) (rounded to the nearest centimetre)
Step 15 ：13. \(\boxed{12.2 \mathrm{~cm} \times 15 \mathrm{~cm}}\) (since the hypotenuse is 12.26 cm, which is less than 12.5 cm)
