Question

1. which group of three squares will form a right triangle when joined at their vertices?

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check option F

For side - lengths \(3\), \(7\), and \(12\): \(3^{2}+7^{2}=9 + 49=58\), and \(12^{2}=144\). Since \(3^{2}+7^{2}
eq12^{2}\), option F is incorrect.

Step3: Check option G

For side - lengths \(6\), \(9\), and \(12\): \(6^{2}+9^{2}=36 + 81 = 117\), and \(12^{2}=144\). Since \(6^{2}+9^{2}
eq12^{2}\), option G is incorrect.

Step4: Check option H

For side - lengths \(8\), \(10\), and \(18\): \(8^{2}+10^{2}=64 + 100 = 164\), and \(18^{2}=324\). Since \(8^{2}+10^{2}
eq18^{2}\), option H is incorrect.

Step5: Check option J

For side - lengths \(8\), \(15\), and \(17\): \(8^{2}+15^{2}=64+225 = 289\), and \(17^{2}=289\). Since \(8^{2}+15^{2}=17^{2}\), option J is correct.

Answer:

J