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Home » Solve for \( x \) in the equation \( 3^2x = 81 \). - Network4

Solve for \( x \) in the equation \( 3^2x = 81 \). - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 \boxed{13\sqrt{3} \text{ square centimeters}}

📌 A right triangle has a hypotenuse of length \( z = 10 \) cm and an inscribed circle with radius \( c = 2 \) cm. What is the ratio of the area of the circle to the area of the triangle?

📌 A_{\text{circle}} = \pi c^2 = \pi (2)^2 = 4\pi

📌 For a right triangle, the radius \( c \) of the inscribed circle is given by:

📌 where \( a \) and \( b \) are the legs. But we also know:

📌 A_{\text{triangle}} = \frac{1}{2}ab = r \cdot s

📌 where \( r = c = 2 \) and \( s = \frac{a + b + z}{2} \) is the semi-perimeter.

📌 Using the identity for right triangles:

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