Question

15）
16）
17）
18）
19）
20）
21）
22）
23）
24）

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse, $a,b$ are legs.

Step2: Solve 15)

Find hypotenuse: $18^2 + 24^2 = 324 + 576 = 900$, $\sqrt{900}=30$

Step3: Solve 16)

Find hypotenuse: $20^2 + 15^2 = 400 + 225 = 625$, $\sqrt{625}=25$

Step4: Solve 17)

Find missing leg: $\sqrt{8^2 - 6^2} = \sqrt{64-36} = \sqrt{28} = 2\sqrt{7}$

Step5: Solve 18)

Find missing leg: $\sqrt{5^2 - 4^2} = \sqrt{25-16} = \sqrt{9}=3$

Step6: Solve 19)

Find missing leg: $\sqrt{50^2 - 14^2} = \sqrt{2500-196} = \sqrt{2304}=48$

Step7: Solve 20)

Find missing leg: $\sqrt{85^2 - 68^2} = \sqrt{7225-4624} = \sqrt{2601}=51$

Step8: Solve 21)

Find missing leg: $\sqrt{25^2 - 24^2} = \sqrt{625-576} = \sqrt{49}=7$

Step9: Solve 22)

Find hypotenuse: $16^2 + 30^2 = 256 + 900 = 1156$, $\sqrt{1156}=34$

Step10: Solve 23)

Find missing leg: $\sqrt{85^2 - 68^2} = \sqrt{7225-4624} = \sqrt{2601}=51$

Step11: Solve 24)

Find missing leg: $\sqrt{70^2 - 42^2} = \sqrt{4900-1764} = \sqrt{3136}=56$

Answer:

1. $30$
2. $25$
3. $2\sqrt{7}$
4. $3$
5. $48$
6. $51$
7. $7$
8. $34$
9. $51$
10. $56$