【Haichuan Teahouse】Brain-teasing Series: Elementary School Questions That Confuse Parents of 211 University Graduates
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?Question: As shown in the figure, the square PQRS has three of its vertices located on the three sides of triangle ABC, with BQ = CQ. Find the area of the square.
This problem is indeed extremely difficult; it’s hard to come up with a solution approach, and it’s also quite complicated.
It seems like Lao Yu is becoming more and more manipulative, always coming up with difficult problems that are tough to solve; P
You’re absolutely right; the key is that parents also have a share. . . . . .
For this problem, although there are answers and explanations available online, it is still very difficult to solve. It seems the result was 27.2; I can’t remember after looking at it. I racked my brains for a long time but came up with no ideas
Let’s explain the approach: taking A as the origin and AB as the positive direction for the X-axis, let ∠CAB = α; this allows us to determine the coordinates of all points, including F, the midpoint of PR. As per the requirements, it must be true that FQ ⊥ PR, which means the product of the slopes of these two lines is -1. Additionally, PR/FQ = 2. By using these conditions, we can find the value of sinα or cosα, and from that determine the length of the square’s diagonals or its area. You can verify this yourselves.
It seems that elementary school students don’t study analytic geometry in the plane; P
I remember learning it in the first year of middle school; now the content for the fifth grade is normal as well. Using plurals would be simpler, but that will have to wait a few more years.
This post was last edited by Yang Qing on 2021-9-16 09:55. I was a middle school student in the 1970s – two years in junior high and two years in senior high. I learned right triangle trigonometry in the second year of junior high, while analytic geometry was taught in senior high. Using your method to determine the coordinates does indeed make it easier to solve the problems. It’s really too difficult to do this for elementary school students; I don’t understand why these people would play games like this with kids. I don’t know how many people in the class are able to think independently and solve this problem.