The hypotenuse (m) and one leg (n) of a right triangle differ by 2. The square of the other side is
A)m+2n
B)m+n
C)2(m-n)
D)2(m+n)
E)m-2n
Work I've done:
x^2+(m-2)^2=m^2
x^2+m^2-4m+4=m^2
x^2+4=4m
x^2=4m-4
Did i do something wrong?
Ok as far as you go.
Now, 2 = m-n, so
4m-4 = 4m-2(m-n) = 4m-2m+2n = 2(m+n)
Note that your basic 6-8-10 triangle works for this.
6^2 + 8^2 = 10^2
6^2 = 2(8+10)
Well, let's go through your work step by step. You correctly set up the equation using the Pythagorean theorem, so good job on that! However, there seems to be a mistake when you simplify:
x^2 + m^2 - 4m + 4 = m^2
Notice that the m^2 terms cancel out, leaving you with:
x^2 - 4m + 4 = 0
Now, to solve for x^2, we need to isolate it:
x^2 = 4m - 4
So far, you're on the right track! Keep going from here to determine the square of the other side of the right triangle.
It seems that you made a mistake in your calculation. Let's go through the solution step-by-step:
We know that the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (m) is equal to the sum of the squares of the lengths of the other two sides (n and x).
So, the equation becomes:
x^2 + n^2 = m^2
Given that the hypotenuse (m) and one leg (n) differ by 2, we can write this as:
m - n = 2 ---> (Equation 1)
Now, let's substitute the value of m from Equation 1 into the Pythagorean equation:
x^2 + n^2 = (n + 2)^2
Expanding the right side:
x^2 + n^2 = n^2 + 4n + 4
Rearranging the equation:
x^2 = 4n + 4
Therefore, the correct answer is A) m + 2n, which is equivalent to 4n + 4.
I hope this clarifies the solution for you!
No, you did not do anything wrong. You correctly set up the equation using the Pythagorean theorem, and derived the equation x^2 = 4m - 4. However, we need to simplify this equation further to find the value of x^2.
To simplify the equation, we can factor out 4 from the right side:
x^2 = 4(m - 1)
Now, let's simplify the right side further:
x^2 = 4m - 4
The right side can be written as 4m - 4 = 4(m - 1). Therefore, the equation can be written as:
x^2 = 4(m - 1)
Now, we need to compare this equation with the answer choices to find the expression that represents the square of the other side. Let's look at the answer choices:
A) m + 2n
B) m + n
C) 2(m - n)
D) 2(m + n)
E) m - 2n
Comparing the equation x^2 = 4(m - 1) with the answer choices, we can see that none of the options match exactly. However, we can simplify answer choice C:
2(m - n) = 2m - 2n
While this expression is not exactly equal to x^2, it is possible that x^2 equals 2m - 2n. Therefore, we can conclude that the answer is C) 2(m - n).