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table salt chemical formula - NBX Soluciones

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 An isosceles triangle has an area of \(48 \, \text{cm}^2\). If the base is increased by \(4 \, \text{cm}\) while the equal sides remain unchanged, by how many square centimeters does the area increase? Assume the equal sides are \(10 \, \text{cm}\) each.

📌 Let the base of the original isosceles triangle be \(b\). The area of the triangle is given by:

📌 \frac{1}{2} \times b \times h = 48

📌 where \(h\) is the height from the vertex to the base. Using the Pythagorean theorem in one of the right triangles formed by the height:

📌 h = \sqrt{10^2 - \left(\frac{b}{2}\right)^2} = \sqrt{100 - \frac{b^2}{4}}

📌 Substituting into the area equation:

📌 \frac{1}{2} \times b \times \sqrt{100 - \frac{b^2}{4}} = 48

📌 Solving for \(b\) involves trial or algebraic manipulation, but instead, let's consider the changes. The new base is \(b + 4\). The new height \(h'\) is:

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