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Home » Substitute \( x = 5 \) into the expressions for length and width: - Aurero

Substitute \( x = 5 \) into the expressions for length and width: - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 #### 785.398

📌 A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Determine if this triangle is a right triangle using the Pythagorean theorem.

📌 \( 7^2 = 49 \) and \( 24^2 = 576 \), so \( 49 + 576 = 625 \).

📌 Since both sides are equal, the triangle is a right triangle.

📌 The sum of the first \( n \) positive integers is given by the formula \( S = rac{n(n + 1)}{2} \). If the sum is 5050, find \( n \).

📌 Set up the equation: \( rac{n(n + 1)}{2} = 5050 \).

📌 Multiply both sides by 2: \( n(n + 1) = 10100 \).

📌 Solve the quadratic equation \( n^2 + n - 10100 = 0 \) using the quadratic formula \( n = rac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

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