SAT Right Triangles - Pythagorean Theorem

Correct Answer: B

Solution:

Tip: If $c^2 > a^2 + b^2,$ then $m\angle C > 90$ and $\triangle ABC$ is obtuse.
We analyze each choice and we select the one that doesn't satisfy the relationship stated in the tip.

(A) $10^2\ \ ?\ \ 5^2+6^2$ yields $100 > 61.$ This triangle is obtuse.
(B) $(6\sqrt{2})^2\ \ ?\ \ 6^2+6^2$ yields $72 = 72.$ This is a right triangle, not obtuse.

We can stop checking here, since (B) is the correct answer, but we show why the rest of the choices are wrong.

(C) $11^2\ \ ?\ \ 8^2+6^2$ yields $121 > 100.$ This triangle is obtuse.
(D) $20^2\ \ ?\ \ 15^2+10^2$ yields $400 > 325.$ This triangle is obtuse.
(E) $(40n)^2\ \ ?\ \ (20n)^2+(30n)^2$ yields $1600n^2 > 1300n^2.$ This triangle is obtuse.

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Incorrect Choices:

(A) , (C) , (D) and (E)
See the Solution for why these choices are wrong.