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Home » Utilisez l’identité \(\sin^2 \theta + \cos^2 \theta = 1\). - Abu Waleed Tea

Utilisez l’identité \(\sin^2 \theta + \cos^2 \theta = 1\). - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 First, calculate the diagonal of the square with side length 5 cm. Using the Pythagorean theorem, the diagonal \(d\) is given by:

📌 d = \sqrt{5^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2} \text{ cm}

📌 The diameter of the circle is equal to this diagonal, \(5\sqrt{2}\) cm. Since the circle is inscribed in a larger square, the side of the larger square is equal to the diameter of the circle. Thus, the side length of the larger square is \(5\sqrt{2}\) cm.

📌 The area \(A\) of the larger square is:

📌 A = (5\sqrt{2})^2 = 25 \times 2 = 50 \text{ square cm}

📌 Thus, the area of the larger square is \(\boxed{50}\) square cm.

📌 An equilateral triangle has a perimeter of 18 cm. If each side is increased by 2 cm, by how many square centimeters does the area increase?

📌 The side length \(s\) of the original equilateral triangle is:

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Second term: \( a_2 = 2 \times 3 + 1 = 7 \)
Third term: \( a_3 = 2 \times 7 + 1 = 15 \)
Fourth term: \( a_4 = 2 \times 15 + 1 = 31 \)
Fifth term: \( a_5 = 2 \times 31 + 1 = 63 \)
A rectangular garden has a length that is 4 meters more than twice its...
Let width = \( w \) meters, then length = \( 2w + 4 \) meters
Perimeter equation: \( 2(w + (2w + 4)) = 68 \)
Simplifying: \( 2(3w + 4) = 68 \)
\( 6w + 8 = 68 \)
\( 6w = 60 \)

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