Question

find the length of lm.

Explanation:

Step1: Apply Pythagorean theorem

In right - triangle $LMN$, if the hypotenuse is $LN = 35$ and one leg is $MN=21$, and we want to find the other leg $LM$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs of the right - triangle. Let $LM = x$, $MN = 21$, and $LN = 35$. Then $x^{2}+21^{2}=35^{2}$.

Step2: Rearrange the formula to solve for $x$

$x^{2}=35^{2}-21^{2}$. First, calculate $35^{2}=35\times35 = 1225$ and $21^{2}=21\times21 = 441$. Then $x^{2}=1225 - 441=784$.

Step3: Take the square root of both sides

$x=\sqrt{784}$. Since $x$ represents the length of a side of a triangle, we take the positive square root. $\sqrt{784}=28$.

Answer:

28