\frac{\sqrt{3} + 1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}(\sqrt{3} + 1)}{3} = \frac{3 + \sqrt{3}}{3}
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- To express this in a single fraction, find a common denominator:
- + \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{\sqrt{3}} + \frac{1}{\sqrt{3}} = \frac{\sqrt{3} + 1}{\sqrt{3}}
- To rationalize the denominator, multiply the numerator and denominator by \(\sqrt{3}\):
- \boxed{\frac{3 + \sqrt{3}}{3}}
- Question:** In a triangle with side lengths 7, 24, and 25 units, find the length of the shortest altitude.
- The triangle with sides 7, 24, and 25 is a right triangle because \(7^2 + 24^2 = 49 + 576 = 625 = 25^2\).
