I just used ordinary geometry to solve it. I know the purpose of the question is to make the student consider the interplay of algebra and geometry, but I opted for a quick solution. A line from B to C, can be found going pythagorean. It is 50.99 and becomes the basis of an isoceles triangle BAC. Lines BC and AC are the equal sides. Each with a length of 36.055. Going Pythagorean again with the triangle on the left, gives line x on the left triangle a distance of 19.99. Rounded to 20.
Where does the 100x come from? The other numbers - 900, 2,500 & 400 - are fairly obvious, if someone is watching the video they probably don't understand were the 100x came from; if they do they are probably not watching the video.
I just used ordinary geometry to solve it. I know the purpose of the question is to make the student consider the interplay of algebra and geometry, but I opted for a quick solution. A line from B to C, can be found going pythagorean. It is 50.99 and becomes the basis of an isoceles triangle BAC. Lines BC and AC are the equal sides. Each with a length of 36.055. Going Pythagorean again with the triangle on the left, gives line x on the left triangle a distance of 19.99. Rounded to 20.
if the sides are equal, and the angle is 90 degrees, you can rotate one triangle to get a rectangle
implies similarity, then congruence
Where does the 100x come from?
The other numbers - 900, 2,500 & 400 - are fairly obvious, if someone is watching the video they probably don't understand were the 100x came from; if they do they are probably not watching the video.
(50 - 𝑥)² = (50 - 𝑥)(50 - 𝑥) = 50*50 - 50𝑥 - 50𝑥 + (-𝑥)(-𝑥) = 2500 - 100𝑥 + 𝑥²
(a - b)² = a² - 2ab + b²
Thanks, I'll write out more details next time