Question

finding lengths sketch the figure that is described. find the requested length. round decimals to the nearest tenth. 21. the side length of an equilateral triangle is 5 centimeters. find the length of an altitude of the triangle.

Explanation:

Step1: Split triangle into 2 right triangles

When drawing an altitude in an equilateral triangle, it splits the base into two equal parts. Each right triangle has hypotenuse $5$ cm, one leg $\frac{5}{2}=2.5$ cm, and the altitude $h$ as the other leg.

Step2: Apply Pythagorean theorem

Use $a^2 + b^2 = c^2$, where $c=5$, $a=2.5$, solve for $h$.
$$h^2 + 2.5^2 = 5^2$$
$$h^2 = 5^2 - 2.5^2$$
$$h^2 = 25 - 6.25 = 18.75$$

Step3: Calculate and round $h$

Take square root and round to nearest tenth.
$$h = \sqrt{18.75} \approx 4.3$$

Answer:

4.3 centimeters