in2ebook Chapter 215: The Triangle Problem
Chapter 215: The Triangle Problem
Although the Dali envoy was unwilling, he had to admire Qin Mufeng's wisdom. After a moment of silence, he spoke again: "Mr. Qin is indeed quick-witted and admirable. However, my Dali Kingdom has another difficult question that I would like to ask Mr. Qin. There is a tall tower, but its exact height is unknown. Next to the tower stands a pole with a length of six zhang. At the same time, the length of the pole's shadow is measured to be two zhang. At this time, the length of the tower's shadow is thirty zhang. How tall is this tower?"
When the ministers of Nanyue heard this question, they fell into deep thought again. Some of them constructed graphs in their minds, trying to find a solution to the problem; others discussed quietly, hoping to brainstorm.
Qin Mufeng narrowed his eyes slightly and thought quickly in his mind. He thought: "This is a problem of similar triangles. The pole and the tower and their shadows form similar triangles respectively, and the corresponding sides are proportional."
Qin Mufeng took a step forward and said calmly, "Mr. Envoy, the answer to this question is ninety feet."
The Dali envoy was slightly stunned and said, "Mr. Qin, please explain your answer."
Qin Mufeng said calmly: "The length of the pole is six zhang, and the length of the shadow is two zhang. The length of the tower's shadow is thirty zhang. Let the height of the tower be x zhang. Because the pole and the tower and their shadows form similar triangles, the corresponding sides are proportional. That is, six to two is equal to x to thirty. By calculation, we can get that x is equal to ninety zhang."
Qin Mufeng's explanation was clear and concise, and everyone present suddenly understood. The Dali envoy was silent for a long time, and then slowly said: "Mr. Qin's wisdom is amazing. Our Dali Kingdom is willing to admit defeat."
The King of Nanyue was filled with joy and said, "My dear Minister Qin, you have once again brought honor to our Nanyue Kingdom. I will definitely reward you handsomely."
Qin Mufeng quickly saluted and said, "Your Majesty, I have no choice but to serve the country. There is no need for rewards."
Warm applause and cheers rang out again in the square. The faces of the ministers of Nanyue State were filled with proud smiles.
The Dali envoy was silent for a moment, then spoke again: "Master Qin, there is another problem in Dali. In Dali, there is a mysterious mine, and a fixed number of miners enter it every day to mine ore. If three miners work together for three days, they can mine 180 kilograms of ore; if five miners work together for two days, they can mine 150 kilograms of ore. Excuse me, how many kilograms of ore can a miner mine in a day?"
The ministers of Nanyue State frowned and thought, and for a moment the square was so quiet that only the slight sound of breathing remained. Qin Mufeng also fell into deep thought, and he quickly analyzed the conditions in the question in his mind.
Qin Mufeng thought: "We can assume that a miner can mine x kilograms of ore a day. Then according to the conditions in the question, we can list a set of equations to solve it."
After some calculations, Qin Mufeng came up with the answer. He took another step forward and said, "Mr. Envoy, the answer to this question is that a miner can mine 20 kilograms of ore a day."
The Dali envoy was slightly stunned and said, "Mr. Qin, please explain your answer."
Qin Mufeng said calmly: "Suppose a miner can mine x kilograms of ore a day. According to the conditions of the question, three miners mined 3 kilograms of ore in three days, and the equation 3x180xx = 20 can be listed, and the solution is x = 5. Let's look at five miners mining 2 kilograms of ore in two days, 150x20xx = , and the solution is x = . So a miner can mine kilograms of ore a day."
Qin Mufeng's explanation was clear and logical, and everyone present nodded frequently. The Dali envoy sighed and said, "Mr. Qin's wisdom has convinced Dali. In this test of wits, Nanyue is the undisputed winner."
The King of Nanyue was filled with joy and said, "My dear Minister Qin, you have once again brought honor to our Nanyue Kingdom. I will definitely reward you handsomely."
Qin Mufeng quickly saluted and said, "Your Majesty, I have no choice but to serve the country. There is no need for rewards."
Warm applause and cheers rang out again in the square. In this test, the Dali Kingdom also looked at the Nanyue Kingdom with new eyes, and the relationship between the two countries also underwent subtle changes unconsciously.