Question

select all the correct answers. based on the side lengths given (a, b, and c), which triangles are right triangles? a = 4, b = 6, c = 8 a = 6, b = 8, c = 10 a = 5, b = 6, c = \sqrt{61} a = 6, b = 9, c = 12

Explanation:

Step1: Recall Pythagorean theorem

$a^{2}+b^{2}=c^{2}$ (c is the longest side)

Step2: Check first option

$4^{2}+6^{2}=16 + 36=52
eq8^{2}=64$

Step3: Check second option

$6^{2}+8^{2}=36 + 64 = 100=10^{2}$

Step4: Check third option

$5^{2}+6^{2}=25+36 = 61=(\sqrt{61})^{2}$

Step5: Check fourth option

$6^{2}+9^{2}=36 + 81=117
eq12^{2}=144$

Answer:

$a = 6,b = 8,c = 10$; $a = 5,b = 6,c=\sqrt{61}$