Question

Which side lengths form a right triangle? Choose all answers that apply: Choose all answers that apply: (Choice A) A 2, 2, \sqrt42,2, 4 ? (Choice B) B 9, 40, 419,40,41 (Choice C) C \sqrt5, 10, \sqrt{125} 5 ? ,10, 125 ? Stuck?Watch a video or use a

Answer 1

Answer:

(B)

Step-by-step explanation:

The given options are:

A. 2, 2, $\sqrt{42}$

B. 9,40, 41

C. $\sqrt{5},10,\sqrt{125}$

In order to prove that the given side lengths form a right triangle, we will satisfy the Pythagoras theorem.

A. $(\sqrt{42})^{2}=(2)^{2}+(2)^{2}$

⇒$42=4+4$

⇒$42=8$

which does not satisfy the theorem, thus this option is incorrect.

B. $(41)^{2}=(9)^{2}+(40)^{2}$

⇒$1681=1600+81$

⇒$1681=1681$

which satisfies the theorem, thus this option is correct.

C. $(\sqrt{125})^{2}=(10)^{2}+(\sqrt{5})^{2}$

⇒$125=100+5$

⇒$125=105$

which does not satisfy the theorem, thus this option is incorrect.