Question

the triangle below is equilateral. find the length of side x to the nearest tenth.
(image of an equilateral triangle with a perpendicular segment of length 4 from one vertex to the opposite side, forming a right triangle with hypotenuse x)
answer attempt 1 out of 2
x = blank box submit answer

Explanation:

Step1: Define triangle properties

The triangle is equilateral, so all sides are length $x$, and the 4-unit segment is the height (altitude) of the equilateral triangle.

Step2: Use altitude formula

For an equilateral triangle, height $h = \frac{\sqrt{3}}{2}x$. Substitute $h=4$:
$$4 = \frac{\sqrt{3}}{2}x$$

Step3: Solve for $x$

Rearrange to isolate $x$:
$$x = \frac{4 \times 2}{\sqrt{3}} = \frac{8}{\sqrt{3}}$$
Rationalize the denominator:
$$x = \frac{8\sqrt{3}}{3}$$

Step4: Calculate decimal value

Compute the numerical approximation:
$$x \approx \frac{8 \times 1.732}{3} \approx \frac{13.856}{3} \approx 4.6$$

Answer:

$x \approx 4.6$