Question

the triangle below is equilateral. find the length of side x to the nearest tenth.
(there is a diagram of an equilateral triangle with a perpendicular segment from a vertex to the opposite side, creating a right triangle with one leg labeled x and the other leg labeled 9.)
answer attempt 1 out of 2
x = blank submit answer

Explanation:

Step1: Define equilateral triangle sides

All sides = 9, so the hypotenuse of the right triangle formed by $x$ is 9, and one leg is $\frac{9}{2}=4.5$.

Step2: Apply Pythagorean theorem

Use $a^2 + x^2 = c^2$, rearrange to solve for $x$.
$x = \sqrt{c^2 - a^2} = \sqrt{9^2 - 4.5^2}$

Step3: Calculate the value

First compute $9^2=81$, $4.5^2=20.25$. Then $81-20.25=60.75$.
$x = \sqrt{60.75} \approx 7.8$

Answer:

$x \approx 7.8$