グローバルビジネスで役立つ数学（40）面積の増分を求める（英語版）

Hi there!

“Off-shore trade” or “tripartite trade” has a nostalgic ring. I was shouldering the critical responsibilities of creating a new business at a trading company every year, and establishing the intermediary trade was one of my missions.

Those businesses include exporting plain paper copiers to India, electronic components to Singapore related to Surface Mount Technology (SMT), and musical instruments to South Africa, too numerous to comprehensively list here.

The day I received a big bounty is still fresh in my memory. I visited almost all acoustic guitar manufacturers in Taiwan and singled out high-quality but low-price makers in two weeks or so. I made all the effort worthwhile and exported dozens of containers to South Africa. Besides receiving such an incentive to enhance my morale, I was given a mission to attend a musical instrument show in Frankfurt, where I was allowed to slack off and hang loose during the fair.

To enlarge the tripartite trade was challenging and rewarding, but today let me try answering the equilateral triangle word problem to find how much larger the triangle has become.

An equilateral triangle of sides \(b\) cm makes its area \(\frac{\sqrt{3}}{4}b^{2}\). How much larger is the area of the larger equilateral triangle than the original one once each side of the latter has been extended by 4 cm?

Here is my solution to the problem.

\(\frac{\sqrt{3}}{4}(b + 4)^{2} – \frac{\sqrt{3}b^{2}}{4}\)
\(= \frac{\sqrt{3}(b^{2} + 8b + 16 – b^{2})}{4}\)
\(= \frac{\sqrt{3}(8b + 16)}{4}\)
\(= \frac{8\sqrt{3}(b + 2)}{4}\)
\(= 2\sqrt{3}b + 4\sqrt{3}\)

∴ The area difference between the two triangles is \((2\sqrt{3}b + 4\sqrt{3})cm^{2}\).

Do I have more areas for improvement?

Stay tuned, and expect to see my next post.

Keep well.

Frank Yoshida

￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣
【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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