Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

k^(2)=m^(2)+n^(2)
For any right triangle, the given equation relates the length of the hypotenuse, 
k, to the lengths of the other two sides of the triangle, 
m and 
n. Which of the following equations correctly gives 
m in terms of 
k and 
n ?
Choose 1 answer:
(A) 
m=k-n
(B) 
m=sqrt(k^(2))-n^(2)
(c) 
m=sqrt(k^(2)-n^(2))
(D) 
m=sqrt(k^(2)+n^(2))

k2=m2+n2 k^{2}=m^{2}+n^{2} \newlineFor any right triangle, the given equation relates the length of the hypotenuse, k k , to the lengths of the other two sides of the triangle, m m and n n . Which of the following equations correctly gives m m in terms of k k and n n ?\newlineChoose 11 answer:\newline(A) m=kn m=k-n \newline(B) m=k2n2 m=\sqrt{k^{2}}-n^{2} \newline(C) m=k2n2 m=\sqrt{k^{2}-n^{2}} \newline(D) m=k2+n2 m=\sqrt{k^{2}+n^{2}}

Full solution

Q. k2=m2+n2 k^{2}=m^{2}+n^{2} \newlineFor any right triangle, the given equation relates the length of the hypotenuse, k k , to the lengths of the other two sides of the triangle, m m and n n . Which of the following equations correctly gives m m in terms of k k and n n ?\newlineChoose 11 answer:\newline(A) m=kn m=k-n \newline(B) m=k2n2 m=\sqrt{k^{2}}-n^{2} \newline(C) m=k2n2 m=\sqrt{k^{2}-n^{2}} \newline(D) m=k2+n2 m=\sqrt{k^{2}+n^{2}}
  1. Given equation: We are given the equation of a right triangle: k2=m2+n2k^2 = m^2 + n^2. We need to solve for mm in terms of kk and nn.
  2. Isolating mm: To isolate mm, we first subtract n2n^2 from both sides of the equation: k2n2=m2k^2 - n^2 = m^2.
  3. Solving for m: Next, we take the square root of both sides to solve for m: m=k2n2m = \sqrt{k^2 - n^2}.
  4. Checking the answer: We check the answer choices to see which one matches our derived equation for m. The correct equation is m=k2n2 m = \sqrt{k^2 - n^2} .

More problems from Compare linear and exponential growth