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5 gallon water bottle with spout - Deep Underground Poetry

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 To find the ratio of the new area to the original area after increasing the side length, we calculate the areas before and after the change.

📌 Original Triangular Area:

📌 The area \( A \) of an equilateral triangle with side \( s \) is given by:

📌 A_{\text{original}} = \frac{\sqrt{3}}{4}s^2

📌 New Triangular Area:

📌 The side length is increased by 50%, so the new side length is \( 1.5s \). The new area is:

📌 A_{\text{new}} = \frac{\sqrt{3}}{4}(1.5s)^2 = \frac{\sqrt{3}}{4} \cdot 2.25s^2 = \frac{2.25\sqrt{3}}{4}s^2

📌 Ratio of New Area to Original Area:

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