Question

quadrilateral jklm is a rhombus. find the missing values. ml = 14 el = 6 kl = 8√10 mk = 8√10

Explanation:

Step1: Recall rhombus properties

In a rhombus, all sides are equal. So, since $JK = 14$, then $ML=JK = 14$ and $KL = JK=14$.

Step2: Recall diagonals property

The diagonals of a rhombus bisect each other. Given $JE = 6$, then $EL=JE = 6$.

Step3: Use Pythagorean theorem

Let the diagonals of the rhombus bisect each other at right - angles. Let half - lengths of diagonals be $a = 6$ and assume the other half - length (not given in the figure but we can find side length relationship) and side length $s = 14$. Using the Pythagorean theorem in one of the four right - triangles formed by the diagonals of the rhombus. Let the other half - diagonal length be $b$. Then $s^{2}=a^{2}+b^{2}$, so $b=\sqrt{s^{2}-a^{2}}=\sqrt{14^{2}-6^{2}}=\sqrt{196 - 36}=\sqrt{160}=4\sqrt{10}$. The length of the diagonal $MK = 2b=8\sqrt{10}$.

Answer:

$ML = 14$, $EL = 6$, $KL = 14$, $MK = 8\sqrt{10}$