Question

1. 7,24,25 right triangle answer by dragging items here 8,15,17 not a right triangle 11,60,61 answer by dragging items here 30,45,60 √105, √120, 15 √150, √125, 18 check answer

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), \(a^{2}+b^{2}=c^{2}\).

Step2: Check 7, 24, 25

Calculate \(7^{2}+24^{2}=49 + 576=625\), and \(25^{2}=625\). So it's a right - triangle.

Step3: Check 8, 15, 17

Calculate \(8^{2}+15^{2}=64 + 225=289\), and \(17^{2}=289\). So it's a right - triangle.

Step4: Check 11, 60, 61

Calculate \(11^{2}+60^{2}=121+3600 = 3721\), and \(61^{2}=3721\). So it's a right - triangle.

Step5: Check 30, 45, 60

Calculate \(30^{2}+45^{2}=900 + 2025=2925\), and \(60^{2}=3600\). So it's not a right - triangle.

Step6: Check \(\sqrt{105}\), \(\sqrt{120}\), 15

Calculate \((\sqrt{105})^{2}+(\sqrt{120})^{2}=105 + 120=225\), and \(15^{2}=225\). So it's a right - triangle.

Step7: Check \(\sqrt{150}\), \(\sqrt{125}\), 18

Calculate \((\sqrt{150})^{2}+(\sqrt{125})^{2}=150+125 = 275\), and \(18^{2}=324\). So it's not a right - triangle.

Answer:

7, 24, 25: Right Triangle
8, 15, 17: Right Triangle
11, 60, 61: Right Triangle
30, 45, 60: Not a Right Triangle
\(\sqrt{105}\), \(\sqrt{120}\), 15: Right Triangle
\(\sqrt{150}\), \(\sqrt{125}\), 18: Not a Right Triangle