Solve for the missing side: simplify the radical
1 answer:
Answer:
Step-by-step explanation:
I will assume the following:
- You know how to use the quadratic formula
- You know how to simplify radicals
- You know how to use the pythagorean theorem.
The challenge of this exercise comes from using the pythagorean theorem and setting up a few equations.
Given that we have a segment 36 units long and another segment that is 16, it is trivial to get the other segment, 20. Additionally, there are two sides that I want to name so that way I can make a couple of substitutions. I will call these side a and side b. (see attachment 1)
Now comes with setting up three equations. I will start with the two smaller triangles, using side a and side b. See attachments 2 and 3.
Now with the big triangle. I will set up one last equation. See attachment 4.
Given what we know about attachment 2 and 3, we can make two substitutions. See attachment 5. I assume you know how to do the rest and arrive at your only real solution.
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Answer:
The correct option is A.
Step-by-step explanation:
Let the vertices of the triangle be ABC.
Draw a perpendicular on AC from B. The height of triangle is represented by the altitude from B.
Area of the triangle is
Therefore option A is correct.
Explanation:
In order to prove that affirmation, we define the function g over the interval [0, 1/2] with the formula
If we evaluate g at the endpoints we have
g(0) = f(1/2)-f(0) = f(1/2) - f(1) (because f(0) = f(1))
g(1/2) = f(1) - f(1/2) = -g(0)
Since g(1/2) = -g(0), we have one chance out of three
- g(0) > 0 and g(1/2) < 0
- g(0) < 0 and g(1/2) > 0
- g(0) = g(1/2) = 0
We will prove that g has a zero on [0,1/2]. If g(0) = 0, then it is trivial. If g(0) ≠ 0, then we are in one of the first two cases, and therefore g(0) * g(1/2) < 0. Since f is continuous, so is g. Bolzano's Theorem assures that there exists c in (0,1/2) such that g(c) = 0. This proves that g has at least one zero on [0,1/2].
Let c be a 0 of g, then we have
Hence, f(c+1/2) = f(c) as we wanted.