Answer: Choice A
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Explanation:
The left side [tex]6^2+8^2[/tex] simplifies to [tex]100[/tex] since [tex]6^2+8^2 = 36+64 = 100[/tex]
The right side is also 100 because [tex]10^2 = 100[/tex]
So [tex]6^2+8^2 = 10^2 [/tex] is a true equation because both sides are the same number.
Therefore, a triangle with sides 6,8,10 is a right triangle. The hypotenuse 10 is the longest side opposite the 90 degree angle. In other words, the 90 degree angle is between the sides 6 ft and 8 ft.
So this is why choice A is the final answer.
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Choice B is false because the inequality [tex]8^2+10^2 < 11^2[/tex] becomes [tex]164 < 121[/tex] which is also false. Even if that inequality was true, we can't use it to form a right triangle. We need both sides to be equal.
Choice C is false because we need to have both sides equal to the same number. We need to have [tex]a^2+b^2 = c^2[/tex] to be true if we want a right triangle with sides a,b,c.
Choice D is false because of the phrasing "Draw any two of the sides with a right angle between them". The 90 degree angle must go between the 6 and the 8, and nowhere else.
