Question

13.c solve the following problems. given: △akl, m∠k = 90°, ak = kl = 2, m ∈ (overline{al}), am = ml find: ml and km answer: ml =, km = clear all

Explanation:

Step1: Find the length of the hypotenuse AL

In right - triangle AKL with $\angle K = 90^{\circ}$, by the Pythagorean theorem $AL^{2}=AK^{2}+KL^{2}$. Since $AK = KL = 2$, then $AL^{2}=2^{2}+2^{2}=4 + 4=8$, so $AL=\sqrt{8}=2\sqrt{2}$.

Step2: Find the length of ML

Given that $AM = ML$ and $AL=AM + ML$, then $ML=\frac{1}{2}AL$. Substituting $AL = 2\sqrt{2}$, we get $ML=\sqrt{2}$.

Step3: Prove that $KM = ML$

In a right - triangle, the median drawn to the hypotenuse is half the length of the hypotenuse. Since $M$ is the mid - point of $AL$ (because $AM = ML$), in right - triangle $AKL$, $KM=\frac{1}{2}AL$. So $KM=\sqrt{2}$.

Answer:

$ML=\sqrt{2}, KM=\sqrt{2}$