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Home » Therefore, the total number of distinct sundaes is \(\boxed280\). - Veritas Home Health

Therefore, the total number of distinct sundaes is \(\boxed280\). - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 First, find the height of the original triangle using the Pythagorean theorem. Let the height from the apex to the base be \( h \), and the half of the base be \( \frac{10}{2} = 5 \) cm. Applying the Pythagorean theorem to one of the right triangles formed:

📌 h = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12 \text{ cm}

📌 The area of the original triangle is:

📌 A_1 = \frac{1}{2} \times 10 \times 12 = 60 \text{ cm}^2

📌 Next, increase the base to 12 cm and find the new height \( h' \) using the same method:

📌 h' = \sqrt{13^2 - \left(\frac{12}{2}\right)^2} = \sqrt{169 - 36} = \sqrt{133}

📌 The area of the new triangle is:

📌 A_2 = \frac{1}{2} \times 12 \times \sqrt{133} = 6\sqrt{133} \text{ cm}^2

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