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Home » We solve this using elimination. Multiply the first equation by 2 and the second by 5: - Carbonext

We solve this using elimination. Multiply the first equation by 2 and the second by 5: - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 An isosceles triangle has side lengths of \(13\) cm, \(13\) cm, and \(10\) cm. Find the length of the altitude to the base of \(10\) cm.

📌 Consider the isosceles triangle with two equal sides of length \(13\) cm and base \(10\) cm. The altitude from the apex (opposite the base) bisects the base into two segments of \(5\) cm each. Let \(h\) be the altitude. Using the Pythagorean Theorem in one of the right triangles formed:

📌 h^2 + 5^2 = 13^2

📌 h^2 + 25 = 169

📌 h^2 = 169 - 25 = 144

📌 h = \sqrt{144} = 12

📌 Therefore, the length of the altitude is \(\boxed{12 \text{ cm}}\).

📌 A square has an area of \(64\) square units. If each side length is increased by \(50\%\), what is the new area of the square?

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