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____ [38]
2 years ago
8

The figure below is a square. Find the length of side x in simplest radical form with a rational denominator.

Mathematics
1 answer:
Mashcka [7]2 years ago
7 0

Answer:

\frac{\sqrt{10}}{2}

Step-by-step explanation:

The diagonal forms two 45-45-90 triangles, with the diagonal being the hypotenuse of both. The Pythagorean Theorem states that a^2+b^2=c^2, where c is the hypotenuse of the triangle, and a and b are the two legs of the triangle.

From the Isosceles Base Theorem, the two legs of a 45-45-90 triangle are always equal. Since we're given a diagonal of \sqrt{5}, we have:

x^2+x^2=\sqrt{5}^2,\\2x^2=5,\\x^2=\frac{5}{2},\\x=\sqrt{\frac{5}{2}}=\frac{\sqrt{5}}{\sqrt{2}}=\frac{\sqrt{5}}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\boxed{\frac{\sqrt{10}}{2}}

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