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k2=m2+n2k^2=m^2+n^2\newlineFor any right triangle, the given equation relates the length of the hypotenuse, kk, to the lengths of the other two sides of the triangle, mm and nn. Which of the following equations correctly gives mm in terms of kk and nn?\newlineChoose 11 answer:\newline(A) m=knm=k-n\newline(B) m=k2n2m=\sqrt{k^{2}}-n^{2}\newline(C) m=k2n2m=\sqrt{k^{2}-n^{2}}\newline(D) m=k2+n2m=\sqrt{k^{2}+n^{2}}

Full solution

Q. k2=m2+n2k^2=m^2+n^2\newlineFor any right triangle, the given equation relates the length of the hypotenuse, kk, to the lengths of the other two sides of the triangle, mm and nn. Which of the following equations correctly gives mm in terms of kk and nn?\newlineChoose 11 answer:\newline(A) m=knm=k-n\newline(B) m=k2n2m=\sqrt{k^{2}}-n^{2}\newline(C) m=k2n2m=\sqrt{k^{2}-n^{2}}\newline(D) m=k2+n2m=\sqrt{k^{2}+n^{2}}
  1. Pythagorean Theorem: We start with the Pythagorean theorem for a right triangle: k2=m2+n2k^2 = m^2 + n^2.
  2. Isolate m2m^2: To solve for mm, we need to isolate m2m^2 on one side of the equation. So we subtract n2n^2 from both sides: k2n2=m2k^2 - n^2 = m^2.
  3. Solve for m: Now we take the square root of both sides to solve for m: m=k2n2m = \sqrt{k^2 - n^2}.

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