Question

maurice brewer-myers - 8.6c mystery pixel art: pythagorean theorem
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f4:f5
1 questions # answer direc
1 6 2 12
1 8 9
3 8 4 5
15 3
5 7.1 6 2.7
11.5 5.7
7 12 8
16 5 12
9 26 10 18
10 24

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Solve for problem 1

For the first triangle with legs \(a = 6\) and \(b = 8\), \(c=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\).

Step3: Solve for problem 2

For the second triangle with legs \(a = 9\) and \(b = 12\), \(c=\sqrt{9^{2}+12^{2}}=\sqrt{81+144}=\sqrt{225}=15\).

Step4: Solve for problem 3

For the third triangle with legs \(a = 8\) and \(b = 15\), \(c=\sqrt{8^{2}+15^{2}}=\sqrt{64 + 225}=\sqrt{289}=17\).

Step5: Solve for problem 4

For the fourth triangle with legs \(a = 3\) and \(c = 5\) (where \(c\) is hypotenuse), \(b=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}=4\).

Step6: Solve for problem 5

For the fifth triangle with legs \(a = 7.1\) and \(b = 11.5\), \(c=\sqrt{7.1^{2}+11.5^{2}}=\sqrt{50.41+132.25}=\sqrt{182.66}\approx13.52\).

Step7: Solve for problem 6

For the sixth triangle with legs \(a = 2.7\) and \(b = 5.7\), \(c=\sqrt{2.7^{2}+5.7^{2}}=\sqrt{7.29+32.49}=\sqrt{39.78}\approx6.31\).

Step8: Solve for problem 7

For the seventh triangle with legs \(a = 12\) and \(b = 16\), \(c=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=20\).

Step9: Solve for problem 8

For the eighth triangle with legs \(a = 5\) and \(b = 12\), \(c=\sqrt{5^{2}+12^{2}}=\sqrt{25+144}=\sqrt{169}=13\).

Step10: Solve for problem 9

For the ninth triangle with legs \(a = 10\) and \(c = 26\) (where \(c\) is hypotenuse), \(b=\sqrt{26^{2}-10^{2}}=\sqrt{676 - 100}=\sqrt{576}=24\).

Step11: Solve for problem 10

For the tenth triangle with legs \(a = 18\) and \(b = 24\), \(c=\sqrt{18^{2}+24^{2}}=\sqrt{324+576}=\sqrt{900}=30\).

Answer:

1. 10
2. 15
3. 17
4. 4
5. Approximately 13.52
6. Approximately 6.31
7. 20
8. 13
9. 24
10. 30