Question

find the length of $overline{st}$.

Explanation:

Step1: Apply Pythagorean theorem

In right - triangle $RST$, if the hypotenuse $RS = 41$ and one leg $RT=40$, and we want to find the other leg $ST$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Let $ST = a$, $RT = b$, and $RS = c$. Then $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

Substitute $c = 41$ and $b = 40$ into the formula: $ST=\sqrt{41^{2}-40^{2}}=\sqrt{(41 + 40)(41 - 40)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$).

Step3: Calculate

$\sqrt{(41 + 40)(41 - 40)}=\sqrt{81\times1}=\sqrt{81}=9$.

Answer:

$9$