Question

The triangle below is equilateral. Find the length of side a in simplest radical form
with a rational denominator.

Answer 1

By using the Pythagorean theorem, we conclude that side x measures (5/2)*√3 units.

How to find the length of side x?

In the image, we can see that the equilateral triangle can be divided into two right triangles.

If each side of the equilateral triangle measures 5 units, then for the right triangles we will have that the hypotenuse measures 5 units, and the bottom side measures half of that: 2.5 units.

Now remember the Pythagorean theorem. It says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.  Then we will have:

$x^2 + 2.5^2 = 5^2$

$x = \sqrt{5^2 - 2.5^2} = \frac{5}{2}\sqrt{3}$

Then we conclude that side x measures (5/2)*√3 units.

If you want to learn more about right triangles:

https://brainly.com/question/2217700

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